Top Banner
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’HQJDQ FDUD SHQGHNDWDQ VHSHUWL LQL VLIDW NHWHUGLIHUHQVLDODQQ\D GDSDW GLEXNWLNDQ VHFDUD ODQJVXQJ EHUGDVDUNDQ 7HRUHPD ’DVDU .DONXOXV )XQJVL/RJDULWPD1DWXUDO 3HUKDWLNDQIXQJVLLQWHJUDOWHQWXGHQJDQOLPLWDWDV I [ W GW W Q [ Q Q [ Q [ Q § ' ¤ ¤ Q ELODQJDQUDVLRQDOQ z -LNDQ ! PDND[ GDSDWGLJDQWLELODQJDQUHDOVHEDUDQJVHGDQJNDQXQWXNQ Q z DJDULQWHJUDOQ\DPHPSXQ\DLDUWLPDND [ KDQ\DGDSDWGLJDQWLELODQJDQUHDOSRVLWLI [ ! 6HNDUDQJNLWDSHUKDWLNDQIXQJVLWHUVHEXWXQWXNQ \DLWX I [ GW W [ [ ! \ \ W [ W 8QWXN[ ! I [! *E \ \ W W 8QWXN[ I [ *E \ \ W [ W 8QWXN [ I [ *E .LWDDNDQPHPEHULQDPDIXQJVL I \DQJPHUXSDNDQVXDWXSULPLWLIGDULIXQJVL \ W W ! 3DGD*E*EGDQ*EGLSHUOLKDWNDQQLODLI [XQWXN[ ! [ GDQ [ %DQGLQJNDQ QLODL IXQJVL LQL GHQJDQ QLODL ORJDULWPD ELDVD GL 608 KDVLOQ\D VHEDJDL EHULNXW /XDV GW W I /XDV GW W GW W I [ [ [ [ /XDV ! GW W I [ [ [
25
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ��������)XQJVL�7UDQVHQGHQ�������)XQJVL�/RJDULWPD�GDQ�(NVSRQHQ.LWD�LQJDW�NHPEDOL�EDKZD�IXQJVL�WUDQVHQGHQ�DGDODK�IXQJVL�\DQJ� WLGDN�GDSDW�GLQ\D�WDNDQ�VHEDJDL�VHMXPODK�EHUKLQJJD�RSHUDVL�DOMDEDU�DWDV�IXQJVL�NRQVWDQ�\ N GDQ�IXQJVLNHVDWXDQ�\ [��6DPSDL�VDDW�LQL�IXQJVL�WUDQVHQGHQ�\DQJ�WHODK�NLWD�NHQDO�DGDODK�IXQJVL�WUL�JRQRPHWUL��\DQJ�WHUGLUL�GDUL�IXQJVL�VLQXV��NRVLQXV��WDQJHQ��NRWDQJHQ��VHFDQ��GDQ�NRVHNDQ�6HNDUDQJ�NLWD�DNDQ�PHPSHODMDUL� IXQJVL� WUDQVHQGHQ� ODLQQ\D��\DLWX� IXQJVL� ORJDULWPD�GDQHNVSRQHQ� �LQYHUVQ\D��� LQYHUV� IXQJVL� WULJRQRPHWUL�� IXQJVL� KLSHUEROLN�� GDQ� LQYHUV� IXQJVLKL�SHUEROLN�� )XQJVL� \DQJ� SHUWDPD� NDOL� GLSHUNHQDONDQ� DGDODK� ORJDULWPD� QDWXUDO�� \DQJGLQ\DWD�NDQ� VHEDJDL� EHQWXN� LQWHJUDO�� 'HQJDQ� FDUD� SHQGHNDWDQ� VHSHUWL� LQL�� VLIDWNHWHUGLIHUHQVLDODQ�Q\D� GDSDW� GLEXNWLNDQ� VHFDUD� ODQJVXQJ� EHUGDVDUNDQ� 7HRUHPD� 'DVDU.DONXOXV�)XQJVL�/RJDULWPD�1DWXUDO 3HUKDWLNDQ�IXQJVL�LQWHJUDO�WHQWX�GHQJDQ�OLPLW�DWDV

I �[�� W GW WQ [ QQ[ Q [ Q�

��

�� ��³ �§©̈̈ ·¹̧̧ ��� � ��Q ELODQJDQ�UDVLRQDO��Qz ��-LND�Q! ���PDND�[ GDSDW�GLJDQWL�ELODQJDQ�UHDO�VHEDUDQJ��VHGDQJNDQ�XQWXN�Q� ���Qz���DJDU�LQWHJUDOQ\D�PHPSXQ\DL�DUWL��PDND�[ KDQ\D�GDSDW�GLJDQWL�ELODQJDQ�UHDO�SRVLWLI��[ !���6HNDUDQJ�NLWD�SHUKDWLNDQ�IXQJVL�WHUVHEXW�XQWXN�Q �����\DLWX

I �[�� GWW[�³ ��[! ��

\ \ �� W

�������������������������[ W8QWXN�[ ! ���I �[��! �

*E��

\ \ �� W

����������� ��������������������������������W8QWXN�[ ���I �[�� �*E��

\\ �� W

������[ ��������������������������������W8QWXN���� [ � ���I �[��� �

*E��.LWD�DNDQ�PHPEHUL�QDPD�IXQJVL�I \DQJ�PHUXSDNDQ�VXDWX�SULPLWLI�GDUL�IXQJVL�\ ��W� W!���3DGD�*E����*E����GDQ�*E���GLSHUOLKDWNDQ�QLODL�I �[��XQWXN�[ ! ���[ ��GDQ���� [ � ��%DQGLQJNDQ� QLODL� IXQJVL� LQL� GHQJDQ� QLODL� ORJDULWPD� ELDVD� GL� 608�� KDVLOQ\D� VHEDJDLEHULNXW�

/XDV ³ GWW I�� � �� � /XDV �

� � �³ ³GWW GWWI [ [[[��� �� ��/XDV !³ GWW I [ [[

� �� ��

Page 2: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���)XQJVL��I �[�� ��[! � )XQJVL�/RJDULWPD�GL�608I �[��� ��XQWXN���� [� � ORJ�[� ��XQWXN���� [� �I �[�� ��XQWXN��������[ � ORJ�[ ��XQWXN��������[ �I �[��! ��XQWXN��������[! � ORJ�[! ��XQWXN��������[! �)HQRPHQD�LQL�PHPSHUOLKDWNDQ�EDKZD�IXQJVL�I PHPSXQ\DL�VLIDW�ORJDULWPD��.LWD�DNDQPHPEHUL� QDPD� IXQJVL� I GHQJDQ� ORJDULWPD� QDWXUDO�� %LOD� GLQDPDNDQ� GHPLNLDQ�� PDNDVHPXD�VLIDW�ORJDULWPD�\DQJ�WHODK�GLSHODMDUL�GL�608�KDUXV�GDSDW�GLEXNWLNDQ�EHUODNX�SDGDIXQJVL�LQL��6HNDUDQJ�NLWD�PXODL�GHQJDQ�GHILQLVL�EHULNXW�'HILQLVL������ )XQJVL ORJDULWPD�QDWXUDO��GLVLQJNDW�OQ��GLWXOLV�I �[�� OQ�[��GLGHILQLVLNDQVHEDJDL I �[�� OQ�[ GWW[

�³ ��[! �'DHUDK�DVDO�IXQJVL�LQL�DGDODK�'I ���f��GDQ�GDHUDK�QLODLQ\D�DGDODK�5I 5�

7XUXQDQ� IXQJVL� ORJDULWPD�QDWXUDO� VHFDUD� ODQJVXQJ� GLSHUROHK� EHUGDVDUNDQ�7HRUHPD�����KDVLOQ\D�VHEDJDL�EHULNXW�7HRUHPD��������-LND�I �[�� OQ�[��PDND�I c �[�� �['LWXOLV�GHQJDQ�FDUD�ODLQ��WHRUHPD�LQL�PHQ\DWDNDQ� �GG[ [ [OQ � ��[! ��6HNDUDQJ� NLWD� DNDQ� PHOLKDW� EDKZD� VLIDW� ORJDULWPD� ELDVD� MXJD� GLSHQXKL� ROHKORJDULWPD�QDWXUDO��SHPEXNWLDQQ\D�GLNHUMDNDQ�GHQJDQ�PHQJJXQDNDQ�7HRUHPD������7HRUHPD����� �D� OQ�DE OQ�D� OQ�E��D! ��GDQ�E! ���E���OQ� DE OQ�D� OQ�E��D! ��GDQ�E! ���F��� OQ�D U� U OQ�D��D! ��GDQ�U ELODQJDQ�UDVLRQDO�%XNWL �D� %HUGDVDUNDQ�7HRUHPD������GDQ�DWXUDQ�UDQWDL�GLSHUROHK� � � �GG[ D[ D[ D [ GG[ [OQ � OQ � � �

$NLEDWQ\D��WHUGDSDW�NRQVWDQWD�F VHKLQJJD�OQ�D [ OQ�[ � F��8QWXN�PH�QHQWXNDQ�F��DPELOODK�[ ���GLSHUROHK�OQ�D OQ���� F��.DUHQD�OQ��� ���PDND� F OQ�D�� -DGL� OQ�D[ OQ� [ � OQ� D� VHKLQJJD� XQWXN� [ EGLSHUROHK�OQ�DE OQ�D� OQ�E���

GWW[�³

Page 3: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ����E��F�

'DUL� DE E� D GLSHUROHK�OQ� DE E� OQ�D��%HUGDVDUNDQ�7HRUHPD�������D�GLSHUROHK�OQ� DE � OQ�E OQ�D��-DGL�WHUEXNWLODK�OQ� DE OQ�D� OQ�E���%HUGDVDUNDQ�7HRUHPD������GDQ�DWXUDQ�UDQWDL�GLSHUROHK� � � � � �GG[ [ [ U [ U[ U [ U GG[ [ GG[ U [U U UOQ � � OQ OQ �� �� �$NLEDWQ\D��WHUGDSDW�NRQVWDQWD�F VHKLQJJD�OQ�[U U OQ�[ � F��8QWXN�PH�QHQWXNDQ�F��DPELOODK�[ ���GLSHUROHK�OQ��� OQ���� F��VHKLQJJD�F ��-DGL�OQ�[U U OQ�[��VHKLQJJD�XQWXN�[ D GLSHUROHK�OQ�D U U OQ�D���

&RQWRK����� 7HQWXNDQ�WXUXQDQ�IXQJVL�\ OQ� ���� [[ �-DZDE GG[ [[ [[

GG[ [[ [[ [ [[[ [ [

OQ � � � � � � � � �� �� � � � �

�� ����� �� � � � ��

�� � � ��

��§©̈ ·¹̧ ����§©̈ ·¹̧ �� � � � ��

�� � �&DUD�ODLQ � � � � � �GG[ [[ GG[ [ [ GG[ [ GG[ [

[ [ [ [[ [ [ [OQ OQ� � OQ� � OQ� � OQ� �

� � � � ��� � � � ��� �� � �� � �� � �� �

��§©̈ ·¹̧ � � � � � � �� � � � � � �� � �� �&RQWRK����� -LND�\ DGDODK�IXQJVL�GDUL�[ VHKLQJJD�\ � OQ�[� \� �[\� �[��WHQWXNDQ�\ c�-DZDE � � � �GG[ \ [ \ [\ GG[ [� �� �OQ � � � � � � � � � �\ GG[ [ [ GG[ \ \ [ \ \ \� � �� � � �� OQ OQ � �� � c� c�

\ [ \ \ [ \ [ \ \ \� �� � � � �� OQ� c � c� c� � �c � � � �\ \ [ [ \ \ \[� � � � � � �OQ� �c � �� �\ [ [ \ \[ \ [ [ \� �� � �� �OQ

7HRUHPD����� � �GG[ [ [ [OQ � z� � GDQ���� � �GG[ X XX X X [ XOQ � � � � c z c� DGD �� � � � � �GG[ [ [ GG[ [ [ GG[ [ [ [ [ [[ [ [[ [[ [OQ � � � � � � � � �� � �� � � � �%XNWL

Page 4: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���%HUGDVDUNDQ�KDVLO�LQL�GDQ�DWXUDQ�UDQWDL�GLSHUROHK� � �GG[ X X GXG[ XXOQ � c� ���

7HRUHPD������GDSDW�PHQJXEDK�SHUNDOLDQ�SHPEDJLDQ�NH�EHQWXN�SHQMXPODKDQ�SHQJX�UDQJDQ��VHKLQJJD�EHUVDPD�GHQJDQ�7HRUHPD������GDSDW�PHQ\HGHUKDQDNDQ�SURVHV�PHQHQ�WXNDQ�WXUXQDQ�IXQJVL��&DUD�GDQ�SURVHVQ\D�GLSHUOLKDWNDQ�GDODP�FRQWRK�EHULNXW�&RQWRK����� 7HQWXNDQ�WXUXQDQ�IXQJVL� \ [[ ��� �� �� �� ��

� � �-DZDE \ [[ \ �� !� �� �� �

� ��� � �

OQ OQ � � OQ OQ�\ [[ [ [ �� � � �� �� �� � � � �� �� � �c � � �\\ [ [ [�� �� � � � � ��� � �

� �c �� � � �§©̈̈ ·¹̧̧\ [[ [ [[� �� �� �� ��� � � � ���� � � �

*UDILN�)XQJVL�/RJDULWPD�1DWXUDO���)XQJVL�I �[�� OQ�[ GWW[�³ ��[! ��WHUGLIHUHQVLDONDQ

SDGD�VHODQJ����f��GHQJDQ�I c�[�� GDQ� I s �[�� ��[! ���6LIDW�VLIDW�IXQJVL�ORJD�ULWPD�QDWXUDO�\DQJ�EHUNDLWDQ�GHQJDQ�JUDILN�IXQJVLQ\D�DGDODK�VHEDJDL�EHULNXW�x NRQWLQX�SDGD�VHODQJ����f��x PRQRWRQ�QDLN�SDGD�VHODQJ����f��x FHNXQJ�NH�EDZDK�SDGD�VHODQJ����f��x OLP OQ OLP OQ[ [[ [o � of �f f� GDQ� �x OQ���| ��������OQ��� �������OQ��|���������OQ��|���������VLIDW�ORJDULWPD�QDWXUDO�GDQ�NDONXODWRU��%HUGDVDUNDQ�LQL��GLSHUROHK�JUDILN�IXQJVLORJDULWPD�QDWXUDO�SDGD�*E����

\� I �[�� OQ�[������������ ������������������������� H [

*E���)XQJVL�(NVSRQHQ�1DWXUDO ,QYHUV�GDUL�IXQJVL�ORJDULWPD�QDWXUDO�GLQDPDNDQ�IXQJVL�HNV�SRQHQ�QDWXUDO��GDQ�GLQ\DWDNDQ�GHQJDQ�HNVS��%HUGDVDUNDQ�VLIDW�IXQJVL�LQYHUV��NLWD�PHP�SXQ\DL�UHODVL [ HNVS�\ � \ OQ�[��[! ��GDQ�\� 5'DUL�VLQL�GLSHUROHKHNVS��OQ�[�� [��[! ����GDQ���OQ��HNVS�\�� \��\� 5

�[ � ��[

Page 5: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���.DUHQD�IXQJVL�ORJDULWPD�QDWXUDO�PRQRWRQ�QDLN��PDND�IXQJVL�LQL�VDWX�NHVDWX��$NLEDWQ\D�SHUVDPDDQ� OQ�[ ��PHPSXQ\DL� MDZDE� WXQJJDO�� VHEXWODK� MDZDEQ\D�ELODQJDQ�H��'L� VLQLNLWD�PHQGHILQLVLNDQ�ELODQJDQ�H DGDODK�ELODQJDQ�UHDO�\DQJ�PHPHQXKL�OQ H ���3HUKDWLNDQEDK�ZD�XQWXN�[ H LQL� HNVS��OQ�H�� HNVS��� H�1LODL�KDPSLUDQ�XQWXN�ELODQJDQ�LUDVLRQDO�H DGDODK��������}3DGD� UHODVL� IXQJVL� LQYHUV� GL� DWDV�� JDQWLNDQ� [ H U�� U ELODQJDQ� UDVLRQDO� NHPXGLDQJXQD�NDQ�VLIDW�OQ�H ��GDQ�7HRUHPD�������F���PDND�NLWD�PHPSXQ\DLH U HNVS��OQ�H U�� HNVS��U OQ�H�� HNVS��U���� �HNVS�U�+DVLO�\DQJ�EHUODNX�XQWXN�ELODQJDQ�UDVLRQDO�U LQL�NLWD�SHUOXDV�XQWXN�ELODQJDQ�UHDO��.DUHQDVHWLDS�ELODQJDQ�UDVLRQDO�DGDODK�ELODQJDQ�UHDO� �5 PHPXDW�4���PDND�NRQVWUXNVL�H[ KDUXVGD�SDW�PHPXDW�KDVLO�LQL��-DGL�NLWD�KDUXV�PHQGHILQLVLNDQH[ HNVS�[��[� 5�$NLEDWQ\D��UHODVL�\DQJ�PHQJNDLWNDQ�IXQJVL�ORJDULWPD�GDQ�HNVSRQHQ�QDWXUDO�PHQMDGL[ H\ � \ OQ�[��[! ��GDQ�\� 5�\DQJ�PHQJKDVLONDQ�UHODVLH OQ�[ [��[! ����GDQ���OQ��H \�� \��\� 5�7XUXQDQ�GDQ�*UDILN�)XQJVL�(NVSRQHQ�1DWXUDO 7XUXQDQ�IXQJVL�\ H[ ODQJVXQJ�GL�SHUROHK�GDUL�VLIDW�LQYHUVQ\D��%HUGDVDUNDQ�UXPXV�WXUXQDQ�IXQJVL�LQYHUV��GDUL�UHODVL\ H[ � [ OQ�\��\! ��GDQ�[� 5 �GHQJDQ� G[G\ \ � GLSHUROHK

c \ G\G[ G[G\ \ \ H[� �� �-DGL�WXUXQDQ�IXQJVL�HNVSRQHQ�QDWXUDO�DGDODK�IXQJVLQ\D�VHQGLUL��%HQWXN�XPXP�GDUL�IXQJVL\DQJ�EHUVLIDW�GHPLNLDQ�DGDODK�\ FH[��F NRQVWDQWD�VHEDUDQJ��WHUPDVXN�F ��&RQWRK����� 7HQWXNDQ�WXUXQDQ�IXQJVL�\ H[ [� OQ �-DZDE � � � �c �§©̈ ·¹̧ �

\ GG[ H H GG[ [ [ H [ [ [ [[H [

[ [ [ [ [ [[ [

� � � �

�� � �

� �OQ OQ OQ

OQ� OQ � OQ

� OQ ��

Page 6: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���6LIDW�GDQ�JUDILN�IXQJVL�HNVSRQHQ�QDWXUDOI �[�� H[ VHFDUD� ODQJVXQJ� GLSHUROHK� GDULLQ�YHUVQ\D��KDVLOQ\D�VHEDJDL�EHULNXW�x NRQWLQX�SDGD�5�x PRQRWRQ�QDLN�SDGD�5�x FHNXQJ�NH�DWDV�SDGD�5�x OLP OLP[ [ [ [H Ho�f of f� GDQ� �%HUGDVDUNDQ�LQL��GLSHUROHK�JUDILN�IXQJVLHNVSRQHQ�QDWXUDO�SDGD�*E����

\\ I �[�� H[�

��������������������������[*E���6LIDW� IXQJVL� HNVSRQHQ� QDWXUDO� EHULNXW� LQL� VHMDODQ� GHQJDQ� VLIDW� IXQJVL� ORJDULWPDQDWXUDO�\DQJ�EHULNDLWDQ�7HRUHPD����� �D� H� �� �F� HH HD

E D E � ��D�E� 5��E� HD�HE HD � E���D�E� 5� �G� �HD�E HDE��D�E� 5�%XNWL �D���.DUHQD�OQ��� ���PDND�H� �����E���0LVDONDQ�V HD GDQ�W HE��PDND�OQ V D GDQ�OQ W E��VHKLQJJD�OQ V� OQ W D� E��$NLEDWQ\D��OQ�VW D� E��NDUHQD�LWX�HD ��E VW HD�HE����F���'DUL�SHPLVDODQ��E���OQ�V� OQ�W OQ� VW D� E��MDGL�HD�E VW HHDE ����G��0LVDONDQ�[ HD GDQ�\ HDE��PDND�OQ�[ D GDQ�OQ�\ DE E OQ�[ OQ�[E�.DUHQD�IXQJVL�ORJDULWPD�QDWXUDO�VDWX�VDWX��PDND�\ [E��MDGL�HDE �HD�E���

)XQJVL�(NVSRQHQ�GHQJDQ�%LODQJDQ�'DVDU�D !�� .LWD�DNDQ�PHPEHUL�DUWL�SDGD�EHVDUDQD[ XQWXN� D ! �� GDQ� [ � 5�� ,QJDWODK� NHPEDOL� UHODVL� D HE � E OQ D�� \DQJPHQJKDVLONDQ D HOQ�D��D !���%HUGDVDUNDQ�7HRUHPD�������G��NLWD�PHPSXQ\DLD[ �H OQ D�� [ H [ OQ�D��D! ��VHKLQJJD�GHILQLVL�XQWXN�IXQJVL�I �[�� D[ DGDODK�VHEDJDL�EHULNXW�'HILQLVL����� x 8QWXN�D! ���NLWD�GHILQLVLNDQ�D[ H[ OQ�D�x )XQJVL� I �[�� D[��D ! ��GDQ�D z ��GLQDPDNDQ� IXQJVL�HNVSRQHQ�GH�QJDQ�ELODQJDQ�GDVDU�D�&DWDWDQ 'DUL�GHILQLVL�D[ H[ OQ�D��D ! ��GLSHUROHK�OQ�D[ OQ�H[ OQ�D� [ OQ�D��VHKLQJJD7HRUHPD�������F��VHNDUDQJ�EHUODNX�XQWXN�HNVSRQHQ�ELODQJDQ�UHDO�6LIDW�)XQJVL�I �[�� D[��D !! ��GDQ�D zz �x 'DHUDK�DVDO�GDQ�GDHUDK�KDVLO�IXQJVL�I DGDODK�'I 5 GDQ�5I ���f��

Page 7: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���x )XQJVL�I NRQWLQX�SDGD�5�x )XQJVL�I PRQRWRQ�QDLN�XQWXN�D! ��GDQ�PRQRWRQ�WXUXQ�XQWXN���� D� ��x )XQJVL�I VHODOX�FHNXQJ�NH�DWDV�SDGD�GDHUDK�DVDOQ\D*UDILN�IXQJVL�I XQWXN�D! ��GLSHUOLKDWNDQ�SDGD�*E����GDQ�XQWXN���� D� ��SDGD�*E����\ I �[�� �D[D !��

���������������������������������[*E������*UDILN�)XQJVL�I �[�� D[��D !! �

\I �[�� �D[����D ���

�����������������������������������������[*E������*UDILN�)XQJVL�I �[�� D[������ D �� �%HQWXN�/LPLW�GDUL�H )XQJVL�I �[�� OQ�[ WHUGLIHUHQVLDONDQ�XQWXN�[ ! ��GHQJDQ�I c�[�� � �[��VHKLQJJD�XQWXN�[ ���I c���� �� OQ�H��.LWD�PHPSXQ\DL

OQ � � OLP � � � � OLP OQ � � OLP OQ � � OQ OLP� �� �H I I K IK KK K KK K K K K K c � � � � �o o o o� � � � � �� � � � � �EHUGDVDUNDQ�GHILQLVL�WXUXQDQ�IXQJVL�I GL����VLIDW�[ OQ�D OQ�D[��GDQ�NHNRQWLQXDQ�IXQJVL�I�.DUHQD�IXQJVL�ORJDULWPD�QDWXUDO�I VDWX�VDWX��PDND�GLSHUROHK�EHQWXN�OLPLW�GDUL�H��\DLWXH KK K �oOLP� � �� �� �'HQJDQ�SHQJJDQWLDQ�Q ��K��PDND�NLWD�PHPSXQ\DL�EHQWXN�OLPLW�ODLQQ\D�GDUL�H��\DLWX� �H Q Q Q �ofOLP � � ������DWDX����� � �H Q Q Q �o�fOLP � � �7XUXQDQ�\ [U��U �� 5 GDQ�[ !! ����6HEHOXP�IXQJVL�ORJDULWPD�QDWXUDO�GDQ�HNVSRQHQ�GL�SHODMDUL��WXUXQDQ�IXQJVL�\ [U GLUDQFDQJ�KDQ\D�XQWXN�U ELODQJDQ�UDVLRQDO��5XPXV�WXUXQ�DQQ\D�DGDODK�\c U[ U����'HQJDQ�VLIDW�VLIDW�ORJDULWPD�GDQ�HNVSRQHQ��WHUQ\DWD�XQWXN�[!��UXPXV�WXUXQDQ�LQL�GDSDW�GLSHUOXDV�XQWXN�ELODQJDQ�UHDO�U��8QWXN�LQL��WXOLVODK\ [ H HU [U U [ OQ OQ ��U� 5 GDQ�[! ��5XPXV�WXUXQDQ�IXQJVL�HNVSRQHQ�PHPEHULNDQc �\ H U[ [ U[ U [U [ U UOQ � � � �)XQJVL�/RJDULWPD�GHQJDQ�%LODQJDQ�'DVDU�D !! ���D zz � )XQJVL�LQL�DWXUDQQ\D�DGDODKI �[�� D ORJ�[��D ! ��GDQ�D z ���\DQJ�GLSHUNHQDONDQ�VHEDJDL�LQYHUV�GDUL�IXQJVL�HNVSRQHQ\ D[��D! ��GDQ�Dz ���%HUGDVDUNDQ�NRQVHS�IXQJVL�LQYHUV��NLWD�PHPSXQ\DL�UHODVL\ D ORJ�[ � [ D \��D! ��GDQ�Dz ��6LIDW�)XQJVL�I �[�� D ORJ�[��D !! ��GDQ�D zz �

��

Page 8: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���x 'DHUDK�DVDO�GDQ�GDHUDK�KDVLO�IXQJVL�I DGDODK�'I ���f��GDQ�5I 5�x )XQJVL�I NRQWLQX�SDGD����f��x )XQJVL�I PRQRWRQ�QDLN�XQWXN�D! ��GDQ�PRQRWRQ�WXUXQ�XQWXN���� D� ��x )XQJVL�I VHODOX�FHNXQJ�NH�EDZDK�SDGD�GDHUDK�DVDOQ\D*UDILNQ\D�GLSHUROHK�GHQJDQ�FDUD�PHQFHUPLQNDQ�JUDILN�IXQJVL�\ D[ WHUKDGDS�JDULV�\ [��XQWXN�D! ��GLSHUOLKDWNDQ�SDGD�*E����GDQ�XQWXN���� D� ��SDGD�*E����\ I �[�� D ORJ�[��D ! �

�����������������������������������������������������������������[

*E����*UDILN�)XQJVL�I �[�� D ORJ�[��D !! �

\

������������������������������������������������������������������[I �[�� D ORJ�[����� D � �*E����*UDILN�)XQJVL�I �[�� D ORJ�[������ D �� �

.DLWDQ�DQWDUD�ORJ�GDQ�OQ���'DUL�[ D \��D ! ���D z ��GLSHUROHK�OQ�[ OQ�D \ \ OQ�D�VHKLQJJD�\ OQOQ [D ��.DUHQD�[ D \ MXJD�PHQJKDVLONDQ�\ D ORJ�[��PDND�GLSHUROHK�NDLWDQDQWDUD�ORJ�GDQ�OQ��\DLWX D ORJ�[ OQOQ [D ��D! ��GDQ�Dz ���������3HQJJXQDDQ�)XQJVL�/RJDULWPD�1DWXUDO3HQJJXQDDQ�/RJDULWPD�1DWXUDO�XQWXN�0HQJKLWXQJ�7XUXQDQ�)XQJVL� \ �� I �[�� J�[�.LWD�PHPSXQ\DL� IXQJVL�\ � I �[�� J�[� \DQJ� WHUGHILQLVL�SDGD�^[ � 5 �� I �[� ! �`�\DQJ�WHUGLIHUHQVLDONDQ�SDGD�GDHUDK�DVDOQ\D�MLND�IXQJVL�I GDQ�J WHUGLIHUHQVLDONDQ��.DUHQD\! ��SDGD�GDHUDK�DVDO�IXQJVLQ\D��PDND�XQWXN�PHQHQWXNDQ�WXUXQDQ�IXQJVL�LQL��WXOLVODKOQ�\ OQ�� I �[�� J�[� J�[��OQ�I �[��'DUL�VLQL�GLSHUROHK c c � c\\ J [ I [I [ J [ I [� � � � �� � � � OQ � � �VHKLQJJD�\c GDSDW�GLWHQWXNDQ�&RQWRK����� 7HQWXNDQ�WXUXQDQ�IXQJVL�\ [VLQ�[�-DZDE )XQJVL�LQL�WHUGHILQLVL�XQWXN�[ ! ���\DQJ�PHQJKDVLONDQ�\ !����'HQJDQ�SURVHV�VH�SHUWL�GL�DWDV� OQ�\ OQ�[VLQ�[ �VLQ�[��OQ�[

Page 9: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���c �\\ [ [ [ [�VLQ �� �FRV � OQ�

\c �VLQ �� �FRV � OQ[ [ [ [��§©̈ ·¹̧[VLQ�[3HQJJXQDDQ�/RJDULWPD�1DWXUDO�XQWXN�0HQJKLWXQJ�/LPLW�)XQJVL�� ���ff���GDQ��ff.LWD�WHODK�PHPSHODMDUL�EHUEDJDL�WHNQLN�SHQ\HOHVDLDQ�PDVDODK�OLPLW�IXQJVL�EHUEHQWXN� � ���f �f����f��GDQ�f � f��6HODLQ�NHHPSDW�EHQWXN�WDN�WHQWX�WHUVHEXW��PDVLK�WHUGDSDWWLJD�EHQWXN�WDN�WHQWX�ODLQQ\D�\DQJ�EHUNDLWDQ�GHQJDQ�OLPLW�IXQJVL�EHUSDQJNDW�IXQJVL��\DLWX����f���GDQ��f��3HQ\HOHVDLDQ�EHQWXN�WDN�WHQWX�LQL�WHQWX�VDMD�GHQJDQ�PHPDQIDDWNDQ�IXQJVLORJDULWPD�QDWXUDO�GDQ�WHRUHPD�/c+RVSLWDO�%HQWXN�WDN�7HQWX��� $NDQ�GLKLWXQJ� � �OLP � � � �[ D J [I [o ��GL�PDQD� OLP � � OLP � �[ D [ DI [ J [o o � ��[ o D GDSDW�GLJDQWL�ROHK�[ o D���[ o D���[ o f��DWDX�[ o �f��&RQWRK����� +LWXQJODK� OLP[ [[o �� �-DZDE 0LVDONDQ�\ [[��NLWD�DNDQ�PHQJKLWXQJ OLP[ \o �� ��'DUL�\ [[ GLSHUROHK�OQ \ [ OQ[� OLP OQ OLP OQ OLP OQ� OLP �� OLP � �[ [ [ [ [\ [ [ [[ [[ [o � o � o � o � o � � � � � � � � �� �� � �.DUHQD�IXQJVL�ORJDULWPD�QDWXUDO�NRQWLQX�SDGD����f���PDND� OQ OLP OLP OQ[ [\ \o � o �

§©̈ ·¹̧ � � ��VHKLQJJD� OLP[ \o �� H� ��&RQWRK����� +LWXQJODK� OLP OQ[ [[o � ��

�� � �-DZDE \ [ [ � �� � OQ

OQ OQ �OQ OQOQ\ [ [ [ [ � ��� � �� �OLP OQ OLP OQOQ OLP �� OLP[ [ [ [\ [ [ [[o � o � o � o � � � � � ��� � �� �� ��OQ OLP[ \o �§©̈ ·¹̧ �

��OLP OLP OQ �[ [ [\ [ H H Ho � o � � � �

�� � � � �

VHKLQJJD

Page 10: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���%HQWXN�WDN�7HQWX�ff� $NDQ�GLKLWXQJ� �OLP � � � �[ D J [I [o ��GL�PDQD� OLP � �[ D I [o f GDQ� OLP � �[ D J [o � ��[ o D GDSDW�GLJDQWL�ROHK�[ o D���[ o D���[ o f��DWDX�[ o �f��&RQWRK����� +LWXQJODK� OLP � � �OQ[ [[of �� � �-DZDE \ ���� [�� � OQ�[OQ�\ OQ����� [�� � OQ�[ OQ � �OQ��[[OLP OQ OLP OQ � �OQ OLP � � �� OLP[ [ [ [\ [[ [[ [ [of of of of � � � � � �� � �

OQ OLP[ \of§©̈ ·¹̧ �OLP OLP � � �OQ[ [ [\ [ H Hof of � � � � �&RQWRK����� +LWXQJODK� � �OLP FRW � OQ

[[[o ��

� �-DZDE \ �FRW�[�� � OQ�[OQ�\ OQ��FRW�[�� � OQ�[ OQ FRWOQ [[� �OLP OQ OLP OQ FRWOQ OLP FRW � FVF� OLP VLQFRV � VLQ�OLP VLQ � FRV �� � �[ [ [ [[

\ [[ [ [[[[ [[[ [ [

o � o � o � o �o �

� � �§©̈ ·¹̧ � �� � �

��

��

��� � � �

.DUHQD� OQ OLP[ \o �§©̈ ·¹̧ �� ���PDND

� �OLP OLP FRW �� OQ[ [

[\ [ H Ho � o � � � �� � � �

%HQWXN�WDN�7HQWX��ff $NDQ�GLKLWXQJ� �OLP � � � �[ D J [I [o ��GL�PDQD� OLP � �[ D I [o � GDQ� OLP � �[ D J [o rf ��[ o D GDSDW�GLJDQWL�ROHK�[ o D���[ o D���[ o f��DWDX�[ o �f��&RQWRK����� +LWXQJODK� � �OLP FRV �[ [[o � �� � �-DZDE � �\ [ [ FRV �� � �

� �OQ OQ FRV OQ FRV OQ FRV�\ [ [ [ [[[ � � � �� � ��

Page 11: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���� � � �OLP OQ OLP OQ FRV OLP FRV � VLQ �[ [ [\ [[ [ [[o o o � � �� � � �� �� � �� �� � �

OQ OLP[ \o§©̈ ·¹̧ �� �� �OLP OLP FRV ��[ [ [\ [ H Ho o � � � � � �� �� �

&RQWRK����� +LWXQJODK� � �OLP �VLQ[ [[o �� �� �-DZDE � �\ [ [ �� ��VLQ

� � � � � �OQ OQ VLQ OQ OQ VLQ�VLQ\ [ [ [ [[[ � � �� � � ��

� �OLP OQ OLP OQ VLQ OLP FRV OLP[ [ [ [\ [[ [[o o o o � �� � �� � � �� �� �� �OQ OLP[ \o§©̈ ·¹̧ �� �� �OLP OLP ��VLQ[ [ [\ [ H Ho o � � � � � �� � �

8QWXN� &RQWRK� ����� VDPSDL� GHQJDQ� ������ EHULODK� DUJXPHQWDVL� GDUL� VHWLDS� ODQJNDK\DQJ�GLJXQDNDQ�GDODP�SURVHV�SHQ\HOHVDLDQQ\D��������6RDO�/DWLKDQ8QWXN� VRDO� �� VDPSDL� GHQJDQ� ��� WHQWXNDQWXUXQDQ� SHUWDPD� GDUL� VHWLDS� IXQJVL� \DQJGLEHUL�NDQ��� I �[�� VLQ�� OQ��[���������� I �[�� H VLQ�[��� I �[�� OQ��VLQ��[������ ��� I �[�� H[ � OQ�[��� I �[�� OQ� �� �

���[[ ���������� I �[�� OQ� ����HH[[ ��� I �[�� OQ����� H[ ��������� I �[�� FRV��[� H[��8QWXN�VRDO���GDQ�����WHQWXNDQ�WXUXQDQ�SHU�WDPD�\c GDUL�VHWLDS�EHQWXN�LPSOLVLW�\DQJ�GLEHUL�NDQ����OQ�[\ \ H[ � � [\����� H[ \ OQ����� [�\��� FRV�\�8QWXN� VRDO� ��� VDPSDL� GHQJDQ� ���

8QWXN�VRDO����VDPSDL�GHQJDQ�����WHQWXNDQWXUXQDQ� SHUWDPD� GDUL� VHWLDS� IXQJVL� \DQJGLEHUL�NDQ���� I �[�� �VLQ�[�[��������������I �[�� [ OQ�[���� I �[�� �FRV�[�VLQ�[����������I �[�� �OQ�[�FRV�[�8QWXN� VRDO� ��� VDPSDL� GHQJDQ� ���KLWXQJODK� OLPLW� GDUL� VHWLDS� EHQWXN� WDN� WHQWX\DQJ�GLEHUL�NDQ���� OLP OQ � �[ [[o ���

�� ������������� OLP[ o f �H[ � [ �� � [���� OLP OQ[ [ [o �� � � ���������������� OLP[o �� �FRW�[�� � OQ�[���� OLP[o �� [ � � OQ�[�������������� ���� OLP[ o f �[�� �� � � OQ�[���� OLP[o� �[� �OQ�[��������������� ���� OLP[o� �VHF�[�� � [�

Page 12: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���JDPEDU�NDQ� JUDILN� VHWLDS� IXQJVL� \DQJGLEHULNDQ� VHWHODK� PHQHQWXNDQ� VHODQJNHPRQRWRQDQ�� WLWLN� HNVWULP�� VHODQJNHFHNXQJDQ��WLWLN�EHORN��GDQ�DVLPWRWQ\D���� I �[�� [ � OQ�[������ �����I �[�� OQ����� [������ I �[�� [ H[� �����I �[�� H [� � ���� I �[�� � OQ�[��� �����I �[�� [ OQ�_[_�

��� OLP�[o �S � �WDQ�[�FRV�[���������� OLP[o� �[ � H[ � ��� � [���� OLP[o� �VLQ� [� WDQ�[��������� ���� OLP[

[[of �§©̈ ·¹̧� � � ���� OLP[of[� � ���� ��OQ�[������������ OLP OQ

[[[of �§©̈ ·¹̧� � �

��������,QYHUV�)XQJVL�7ULJRQRPHWUL.LWD� LQJDW�NHPEDOL�EDKZD�V\DUDW�DJDU�IXQJVL� I PHPSXQ\DL� LQYHUV�DGDODK�VDWX�VDWX�\DLWX�PHPHQXKL�V\DUDW�I �X�� I �Y���� X Y XQWXN�VHWLDS�X��Y � 'I ��,QYHUV�GDUL�IXQJVLI ��'I o 5I DGDODK�IXQJVL�I �� ��5I o 'I \DQJ�PHPHQXKL�UHODVL�\ I �[���� [ I ���\��GHQJDQ�[ � 'I GDQ�\ � 5I��)XQJVL�WULJRQRPHWUL�VHPXDQ\D�SHULRGLN��VHKLQJJD�WLGDN�VDWX�VDWX��7HWDSL��GDHUDK�DVDO�IXQJVLQ\D�GDSDW�GLEDWDVL�SDGD�VHODQJ�WHUWHQWX�DJDU�PHPSXQ\DLLQYHUV�� 3HPLOLKDQ� VHODQJ� GDHUDK� DVDO� IXQJVLQ\D�GLEXDW� DJDU� DQWDUD� LQYHUV� WULJRQRPHWULGD�SDW�GLNDLWNDQ�GDQ�UXPXV�NDONXOXV�GLIHUHQVLDOQ\D�GDSDW�GLNRQVWUXNVL�,QYHUV�)XQJVL�6LQXV�GDQ�)XQJVL�.RVLQXV ,QYHUV�IXQJVL�VLQXV��GLWXOLV�\ VLQ�� [��DWDX\ DUF�VLQ�[��DGDODK�IXQJVL�\DQJ�PHPHQXKL\ VLQ�� [ � [ VLQ�\��_[_ d ��GDQ�_\_ d �� S �,QYHUV�IXQJVL�NRVLQXV��GLWXOLV�\ FRV�� [ DUF�FRV�[��DGDODK�IXQJVL�\DQJ�PHPHQXKL\ FRV�� [ � [ FRV�\��_[_ d ��GDQ���d \d S�.DLWDQ�DQWDUD�LQYHUV�IXQJVL�VLQXV�GDQ�IXQJVL�NRVLQXV�GLEHULNDQ�GDODP�WHRUHPD�EHULNXW�7HRUHPD����� FRV�� [� VLQ�� [ �� S ��_[_ d ��%XNWL \ FRV�� [ � [ FRV�\ VLQ�� �� S � \���� �� S � \ VLQ�� [� \� VLQ�� [ �� S � FRV�� [� VLQ�� [ �� SNDUHQD���d \d S � � �� S d �� S � \d �� S � _ �� S � \_ d �� S ��%HUGDVDUNDQ�VLIDW�IXQJVL�LQYHUV��JUDILN�\ VLQ�� [ GLSHUROHK�GHQJDQ�PHQFHUPLQNDQJUDILN�\ VLQ�[��[� >� �� S � �� S @ WHUKDGDS�JDULV�\ [��'HPLNLDQ�MXJD�JUDILN�\ FRV��[��\DQJ�GLSHUROHK�GHQJDQ�PHQFHUPLQNDQ�JUDILN�\ FRV�[��[� >��S@�WHUKDGDS�JDULV�\ [��*UDILN�LQYHUV�IXQJVL�VLQXV�GDQ�NRVLQXV�GLSHUOLKDWNDQ�SDGD�*E�����GDQ�*E����

Page 13: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���

\S�� \ [��S�����������������������������������������������S��������[

���S��

*E�����*UDILN�)XQJVL�6LQXV�GDQ�,QYHUVQ\D

\S\ [

S������������������������������������S��������������������������S [

��*E�����*UDILN�)XQJVL�.RVLQXV�GDQ�,QYHUVQ\D

,QYHUV�)XQJVL�7DQJHQ�GDQ�)XQJVL�.RWDQJHQ ,QYHUV�IXQJVL�WDQJHQ��GLWXOLV�\ WDQ�� [�DWDX�\ DUF�WDQ�[��DGDODK�IXQJVL�\DQJ�PHPHQXKL\ WDQ�� [ � [ �WDQ�\��[� 5 GDQ�_\_ � �� S �,QYHUV�IXQJVL�NRWDQJHQ��GLWXOLV�\ FRW�� [ DUF�FRW�[��DGDODK�IXQJVL�\DQJ�PHPHQXKL\ FRW�� [� [ �FRW�\��[� 5 GDQ���� \� S�.DLWDQ� DQWDUD� LQYHUV� IXQJVL� WDQJHQ� GDQ� IXQJVL� NRWDQJHQ� GLEHULNDQ� GDODP� WHRUHPDEHULNXW�7HRUHPD����� FRW�� [� WDQ�� [ �� S ��[� 5�%XNWL \ FRW�� [ � [ FRW�\ WDQ�� �� S � \���� �� S � \ WDQ�� [� \� WDQ�� [ �� S � FRW�� [ ��WDQ�� [ �� SNDUHQD���� \� S � � �� S � �� S � \� �� S � _ �� S � \_ � �� S ���%HUGDVDUNDQ� VLIDW� IXQJVL� LQYHUV�� JUDILN� \ WDQ�� [ GLSHUROHK� GHQJDQ� PHQFHUPLQNDQJUDILN�\ WDQ�[��[ � �� �� S � �� S � WHUKDGDS�JDULV�\ [��'HPLNLDQ�MXJD�JUDILN�\ FRW��[��\DQJ�GLSHUROHK�GHQJDQ�PHQFHUPLQNDQ�JUDILN�\ FRW�[��[ � ���S��WHUKDGDS�JDULV�\ [��*UDILN�LQYHUV�IXQJVL�WDQJHQ�GDQ�NRWDQJHQ�GLSHUOLKDWNDQ�SDGD�*E�����GDQ�*E����

\ FRV�[

\ FRV�� [\ VLQ�� [\ VLQ [

Page 14: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���

\\ [

S��\ WDQ�� [

�S���������������� �����������S����������������������[�S��

*E�����*UDILN�)XQJVL�7DQJHQ�GDQ�,QYHUVQ\D

\\ FRW�[ \ �[S

�����������������������S [

*E�����*UDILN�)XQJVL�.RWDQJHQ�GDQ�,QYHUVQ\D,QYHUV�)XQJVL�6HNDQ�GDQ�)XQJVL�.RVHNDQ ,QYHUV�IXQJVL�VHNDQ��GLWXOLV�\ VHF�� [�DWDX�\ DUF�VHF�[��DGDODK�IXQJVL�\DQJ�PHPHQXKL\ VHF�� [ � [ VHF�\��_[_ t ��GDQ���d \d S��\z �� S �'DUL� [ \ \ VHF FRV� GLSHUROHK�FRV \ �[ � �d \dS��\z �� S ��VHKLQJJD�\ FRV�� �[ �,QL�PHQJDNLEDWNDQ,QYHUV�IXQJVL�NRVHNDQ��GLWXOLV�\ FVF�� [ DUF�FVF�[��DGDODK�IXQJVL�\DQJ�PHPHQXKL\ FVF�� [ � [ FVF�\��_[_ t ��GDQ�_\_ d �� S ��\z �'DUL� [ \ \ FVF VLQ� GLSHUROHK�VLQ�\ �[ ��_\_ d �� S ��\ z ���VHKLQJJD�\ VLQ�� �[ �,QL�PHQJDNLEDWNDQ.DLWDQ�DQWDUD�LQYHUV�IXQJVL�VHNDQ�GDQ�IXQJVL�NRVHNDQ�GLEHULNDQ�GDODP�WHRUHPD�EHULNXW�7HRUHPD����� VHF�� [� FVF�� [ �� S ��_[_ t ��%XNWL 'HQJDQ�PHQJJXQDNDQ�7HRUHPD������ODQJVXQJ�GLSHUROHKVHF�� [� FVF�� [ FRV�� �[ � VLQ�� �[ �� S ��_[_ t ����

VHF FRV � �� � t� � � �[ [ [

FVF VLQ � �� � t� � � �[ [ [

\ WDQ�[\ FRW�� [

S��S��

Page 15: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���%HUGDVDUNDQ� VLIDW� IXQJVL� LQYHUV�� JUDILN� \ VHF�� [ GLSHUROHK� GHQJDQ� PHQFHUPLQNDQJUDILN�\ VHF�[��[ � >��S@��[ z �� S WHUKDGDS�JDULV�\ [��'HPLNLDQ�MXJD�JUDILN�\ FVF�� [��\DQJ�GLSHUROHK�GHQJDQ�PHQFHUPLQNDQ�JUDILN�\ FVF�[��[ � >� �� S � �� S @��\ z �WHUKDGDS�JDULV�\ [��*UDILN�LQYHUV�IXQJVL�VHNDQ�GDQ�NRVHNDQ�GLSHUOLKDWNDQ�SDGD�*E����GDQ�*E���� \ \ VHF�[S \ [

\ VHF�� [ S�������������������������S����������S [��

\ VHF�[

*E�����*UDILN�)XQJVL�6HNDQ�GDQ�,QYHUVQ\D

\\ FVF�[ \ [S������������������������ \ FVF�� [

�S���������������� ����������S�����������������������[\ FVF�� [ ���S��\ FVF�[

*E�����*UDILN�)XQJVL�.RVHNDQ�GDQ�,QYHUVQ\D&RQWRK��������7XQMXNNDQ�EDKZD� � � �� � �� ��WDQ WDQ� �� S �-DZDE���0LVDONDQ�[ ��WDQ�� �� GDQ�\ WDQ�� �� ��DNDQ�GLEXNWLNDQ�[� \ �� S �.DUHQD�[ ��WDQ�� �� ��PDND�WDQ�� �� �� [ ��VHKLQJJD�WDQ� �� [ �� ��,QL�PHQJDNLEDWNDQWDQ WDQWDQ �[ [ [ � � �� ����� ��

������ �

.DUHQD�\ WDQ�� �� ��PDND�WDQ�\ �� ��%HUGDVDUNDQ�UXPXV�WDQJHQ�MXPODK�GXD�VXGXW�WDQ � � WDQ WDQWDQ WDQ �[ \ [ \[ \� �� �� �

�� � ��� ���� ���� ����� ��� �

,QL�PHQJDNLEDWNDQ�[� \ �� S ��VHKLQJJD�WHUEXNWLODK� � � �� � �� ��WDQ WDQ� �� S ���7XUXQDQ�,QYHUV�)XQJVL�7ULJRQRPHWULx 7XUXQDQ�IXQJVL \ VLQ���� [ 'DUL�\ VLQ�� [ � [ VLQ�\��_[_d ��GDQ�_\_d �� SGDQ�UXPXV�WXUXQDQ�IXQJVL�LQYHUV�GLSHUROHK

c � �\ G\G[ G[G\ \ \ [� � �� ��� �FRV VLQ ��_[_ � ��

\ VHF�� [

Page 16: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���x 7XUXQDQ�IXQJVL \ FRV���� [ 'DUL�\ FRV�� [ �� S � VLQ�� [��_[_ d ��GLSHUROHK� �c � ���\ G\G[ GG[ [ [�� � ���S VLQ ��_[_ � ��x 7XUXQDQ�IXQJVL \ WDQ���� [ 'DUL�\ WDQ�� [ � [ WDQ�\��[ � 5 GDQ�_\_ � �� SGDQ�UXPXV�WXUXQDQ�IXQJVL�LQYHUV�GLSHUROHK

c � �\ G\G[ G[G\ \ \ [� � �� ��� � �VHF WDQ ��[� 5�x 7XUXQDQ�IXQJVL \ FRW���� [ 'DUL�\ FRW�� [ �� S � WDQ�� [��[� 5 GLSHUROHK� �c � ���\ G\G[ GG[ [ [�� � ���S WDQ ��[� 5�x 7XUXQDQ�IXQJVL \ VHF���� [ 'DUL�\ VHF�� [ FRV�� �[ ��_[_ t ��GLSHUROHK

c �� � � �\ G\G[ [ [ [[ [ [ [�� � � � � ��� � � �� ��_[_ ! ��

x 7XUXQDQ�IXQJVL \ FVF���� [ 'DUL�\ FVF�� [ �� S � VHF�� [��_[_ t ��GLSHUROHK� �c � � ��\ G\G[ GG[ [ [ [�� � �� �S VHF ��_[_ ! ��'HQJDQ�GHPLNLDQ�NLWD�PHPSXQ\DL�WHRUHPD�EHULNXW��WHQWDQJ�WXUXQDQ�LQYHUV�IXQJVL�WULJR�QRPHWUL7HRUHPD��������7XUXQDQ�,QYHUV�)XQJVL�7ULJRQRPHWUL�D��� � �GG[ [ [VLQ� �� ��� ��_[_ � ���E��� � �GG[ [ [FRV� ��� ��� ��_[_ � ���F��� � �GG[ [ [WDQ� �� ��� ��[� 5�

�G��� � �GG[ [ [FRW� ��� ��� ��[� 5��H��� � �GG[ [ [ [VHF� �� �� � ��_[_ ! ���I ��� � �GG[ [ [ [FVF� � �� �� � ��_[_ ! ��

&RQWRK��������7XQMXNNDQ�EDKZD� � �GG[ [ [ [VHF� �� �� � ��_[_ ! ��-DZDE���%HUGDVDUNDQ�7HRUHPD�������H���DWXUDQ�UDQWDL�GDQ�WXUXQDQ�QLODL�PXWODN�GLSHUROHK

Page 17: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���� � � �GG[ [ [ [ GG[ [ [ [ [[[[ [ [ [ [VHF � �

� �� � �

� � !� � �

� � �

� � � �� � � �

&RQWRK����� %XNWLNDQ� � �VLQ WDQ� �� ��[ [ [ �-DZDE 0LVDONDQ�\ WDQ�� [��PDND�[ WDQ�\ VLQFRV\\ ��GHQJDQ�_\_ �� �� S ��%HUGDVDU�NDQ�LQL�GDQ�UXPXV�WULJRQRPHWUL�GLSHUROHK� �VLQ WDQ VLQ �WDQ � �FRV � WDQVHF WDQVHF WDQWDQ� � �� � � �� �[ \ \ \ \\ \\ \ \ [ [ �VHKLQJJD�WHUEXNWLODK�\DQJ�GLLQJLQNDQ���&RQWRK����� 7HQWXNDQ�WXUXQDQ�IXQJVL�WDQ�� \ OQ�[\�-DZDE� 7HQWXNDQ�WXUXQDQ�GDUL�NHGXD�UXDV�SHUVDPDDQ�\DQJ�GLEHULNDQ�GHQJDQ�PHQJDQJ�JDS�\ IXQJVL�GDUL�[ NHPXGLDQ�Q\DWDNDQ�\ c VHEDJDL�IXQJVL�GDUL�[ GDQ�\�� ��� ��� c c�\ \ [ \ [ \ \� �

[ \ \ [ \ \ [ \ \ \c c� � c�� �c � � �\ [ \ [ [ \ \ \� �� �� �� �c �� �\ \ \[ \ \���� �

&RQWRK� ����� � 7HQWXNDQ� GDHUDK� DVDO�� GDHUDK� QLODL�� GDQ� LQYHUV� IXQJVL� I �[�� FRV��� ��[� �-DZDE $JDU� I �[��� 5�� V\DUDWQ\D�DGDODK� � �� �[� d ��6HOHVDLNDQ�SHUWDNVDPDDQ�QLODLPXWODN�LQL� GLSHUROHK����d �[ � ��d ���$NLEDWQ\D����d �[ d �� VHKLQJJD����d [ d��-DGL�GDHUDK�DVDO�IXQJVL�I DGDODK�'I >����@�

.DUHQD�XQWXN���d [d ��EHUODNX� � �� �[� d ��PDND� � � ���d � d�I [ [� � FRV S �VHKLQJJD�GDHUDK�QLODL�IXQJVL�I DGDODK�5I >��S@�8QWXN�PHQHQWXNDQ�LQYHUV�IXQJVL�I��WXOLVODK�\ I �[�� FRV�� � ��[� GDQ�Q\DWDNDQ�[GDODP�\��GLSHUROHK

Page 18: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���� ��[ \� FRV�[� �� FRV�\[ � �� FRV�\� � �� �-DGL�LQYHUV�IXQJVL�I DGDODK�I ���[�� � �� FRV�[� � �� ����d [d S��������6RDO�/DWLKDQ8QWXN� VRDO� �� VDPSDL� GHQJDQ� ��� WXQMXNNDQNHEHQDUDQ�VHWLDS�SHUQ\DWDDQ�\DQJ�GLEHULNDQ��� FRV��� VLQ�� �� �� �� �� ����FRV��FRV�� �� � VLQ�� ���� �� ���� ��� WDQ�� �� � WDQ�� �� �� S��� VLQ��FRV�� �� �� ��� ��VLQ�� �� �� � �� ��� FRV FRV �� �� � ��� � �� ���� � S�� VLQ��� WDQ�� ����� � �� �8QWXN� VRDO� �� VDPSDL� GHQJDQ� ���� EXNWLNDQVHWLDS�NHVDPDDQ�\DQJ�GLEHULNDQ�� ��� FRV WDQ� �� ���[ [ �

���FRV����VLQ�� [�� ��� �[��� ��� WDQ VLQ� �� ��[ [ [ �� ���� VHF FRV� �� �� �� �[ [ �

8QWXN�VRDO����VDPSDL�GHQJDQ�����EXNWLNDQVHWLDS�NHVDPDDQ�\DQJ�GLEHULNDQ���� VLQ�� ��[�� �VLQ�� [���� FRV�� ��[�� S � FRV�� [���� WDQ�� ��[�� �WDQ�� [���� FRW�� ��[�� S � FRW�� [���� VHF�� ��[�� S � VHF�� [���� VLQ�� ��[�� �VLQ�� [�8QWXN�VRDO����VDPSDL�GHQJDQ�����WHQWXNDQGDHUDK� DVDO�� GDHUDK� QLODL�� LQYHUV�� GDQ� WXUXQDQGDUL�VHWLDS�IXQJVL�\DQJ�GLEHULNDQ���� I �[�� ��VLQ�� �� [���� I �[�� ��FRV�� �� � �� �[� ���� I �[�� FRV�� �OQ [ ����� I �[�� WDQ�� ���� [� ����� I �[�� ��FRW�� ���� [ ����� I �[�� ��VHF�� [ ���������)XQJVL�+LSHUEROLN�GDQ�,QYHUVQ\D.LWD� LQJDW� NHPEDOL� NRQVHS� IXQJVL� WULJRQRPHWUL� \DQJ� GLNDLWNDQ� GHQJDQ� OLQJNDUDQVDWX�DQ��3DGD�*E����� WLWLN�3 WHUOHWDN�SDGD� OLQJNDUDQ�X� � Y� ��GDQ�[ ��23�VE�[SRVLWLI�� Y�W

W�� ����������V ����X��*E���

-LND�NRRUGLQDW�WLWLN�3 DGDODK��V�W���IXQJVL�VLQXV�GDQ�NRVLQXVGLUDQFDQJ�VHEDJDLFRV�[ V GDQ�����VLQ�[ W�)XQJVL� WULJRQRPHWUL� ODLQQ\D� GLUDQFDQJ� VHEDJDL� NRPELQDVLGDUL�VLQXV�GDQ�NRVLQXV��\DLWXWDQ VLQFRV � FRW FRVVLQ � VHF FRV � FVF VLQ[ [[ W [[ [ [ [ [ � � �.DUHQD��V�W��WHUOHWDN�SDGD�OLQJNDUDQ��PDND�V� � W� ���VHKLQJJD�FRV��[� VLQ��[ ��

3�V�W�

Page 19: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���)XQJVL�KLSHUEROLN�GLNRQVWUXNVL�GHQJDQ�JDJDVDQ�PHQJJDQWLNDQ�OLQJNDUDQ�VDWXDQ�ROHKKLSHUERO�VDWXDQ��-LND�WLWLN�3�V�W��WHUOHWDN�SDGD�KLSHUERO�X� � Y� ���NLWD�DNDQ�PHQGHILQL�VLNDQ�FRVK�[ X GDQ�VLQK�[ W��GL�PDQD�FRVK�GDQ�VLQK�PHQ\DWDNDQ�NRVLQXV�GDQ�VLQXVKLSHUEROLN��7HUQ\DWD�EDKZD�VDODK�VDWX�SLOLKDQ�XQWXN�FRVK�[ GDQ�VLQK�[ DGDODK�NRPELQDVLGDUL�IXQJVL�HNVSRQHQ�QDWXUDO��\DLWX�FRVK�[ �� �H[� H�[ ��GDQ�VLQK�[ �� �H[� H�[ ��

'HILQLVL�)XQJVL�+LSHUEROLN )XQJVL�KLSHUEROLN�GLGHILQLVLNDQ�VHEDJDL�EHULNXW�x )XQJVL�NRVLQXV�KLSHUEROLN ����I �[�� FRVK�[ �� �H[� H�[ ����[� 5�x )XQJVL�VLQXV�KLSHUEROLN� � I �[�� VLQK�[ �� �H[� H�[ ����[� 5�x )XQJVL�WDQJHQ�KLSHUEROLN ����I �[�� WDQK�[ VLQKFRVK[[ ���[� 5�x )XQJVL�NRWDQJHQ�KLSHUEROLN ����I �[�� FRWK�[ FRVKVLQK [[ ���[z ��x )XQJVL�VHNDQ�KLSHUEROLN ����I �[�� VHFK�[ �FRVK [ ���[� 5�x )XQJVL�NRVHNDQ�KLSHUEROLN ����I �[�� FVFK�[ �VLQK [ ���[z ��

'DODP�EHQWXN�HNVSRQHQ��IXQJVL�WDQJHQ��NRWDQJHQ��VHNDQ��GDQ�NRVHNDQ�GDSDW�GLWXOLVVHEDJDL�EHULNXW�x WDQK [ H HH H HH[ [

[ [[[ �� ���

��� �� ��[� 5�

x FRWK [ H HH H HH[ [[ [

[[ �� ���

��� �� ��[z ��

x VHFK�[ H H HH[ [[

[ � ��� � �� ��[� 5�x FVFK�[ H H HH[ [

[[ � ��� � �� ��[z ��

7XUXQDQ�)XQJVL�+LSHUEROLN� 7XUXQDQ�IXQJVL�NRVLQXV�GDQ�VLQXV�KLSHUEROLN�GLSHUROHKGDUL�EHQWXN�HVNSRQHQQ\D�� VHGDQJNDQ� WXUXQDQ�KLSHUEROLN� ODLQQ\D�GLSHUROHK�EHUGDVDUNDQDWXUDQ�PHQHQWXNDQ�WXUXQDQ��+DVLOQ\D�GLEHULNDQ�GDODP�WHRUHPD�EHULNXW�7HRUHPD����� 7XUXQDQ�)XQJVL�+LSHUEROLN�D� � �GG[ [ [FRVK VLQK ��E� � �GG[ [ [VLQK FRVK ��F� � �GG[ [ [WDQK VHFK� �

�G� � �GG[ [ [FRWK �FVFK� ��H��� � �GG[ [ [ [VHFK VHFK � WDQK ��I ��� � �GG[ [ [ [FVFK FVFK � FRWK �

Page 20: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���*UDILN�)XQJVL�+LSHUEROLN 3DGD�GDHUDK�DVDOQ\D��VHPXD�IXQJVL�KLSHUEROLN�NRQWLQX�GDQWHUGLIHUHQVLDONDQ� 6HWHODK� WXUXQDQ� SHUWDPD� GDQ� NHGXD� GDUL� IXQJVLQ\D� GLWHQWXNDQ�GLSHUROHK� VHODQJ� NHPRQRWRQDQ�� WLWLN� HNVWULP� EHVHUWD� MHQLVQ\D�� GDQ� VHODQJ� NHFHNXQJDQEHVHUWD�WLWLN�EHORNQ\D��.HPXGLDQ��WHQWXNDQ�OLPLW�WDN�KLQJJD�GDQ�GL�WDN�KLQJJDQ\D�XQWXNPHPSHUROHK�DVLPWRW�IXQJVLQ\D��%HUGDVDUNDQ�LQL��NHUMDNDQ�SURVHVQ\D����GLSHUROHK�JUDILNIXQJVL�KLSHU�EROLN�\DQJ�GLSHUOLKDWNDQ�SDGD�*E�����*E�����GDQ�*E����

\ \ FRVK [\ VLQK [

�������������������[

*E���

\\ FRWK [

� \ WDQK [\ WDQK [ �������������������������[��\ FRWK [

*E���

\\ FVFK�[

\ VHFK [����������������������������[

\ FVFK�[*E���

6LIDW� )XQJVL�+LSHUEROLN� � � 6HMDODQ� GHQJDQ� VLIDW� IXQJVL� WULJRQRPHWUL�� NLWD�PHPSXQ\DLVLIDW�\DQJ�VHUXSD�XQWXN�IXQJVL�KLSHUEROLN� 6HPXD�VLIDW�SDGD�WHRUHPD�EHULNXW�GLEXNWLNDQGHQJDQ�GHILQLVL�IXQJVL�KLSHUEROLN�GDQ�VLIDW�IXQJVL�HNVSRQHQ��WHNQLVQ\D�GLVHUDKNDQ�SDGDSHPEDFD�7HRUHPD��������6LIDW�)XQJVL�+LSHUEROLNx FRVK���[�� FRVK�[�x VLQK���[�� �VLQK�[�x WDQK���[�� �WDQK�[�x FRWK���[�� �FRWK�[�x VHFK���[�� VHFK�[�x FVFK���[�� �FVFK�[�x WDQK�[ �FRWK [ �x FRVK�[� VLQK�[ H[�x FRVK�[� VLQK�[ H�[�x FRVK��[� VLQK��[ ��x ��� WDQK��[ VHFK��[�x FRWK��[� �� FVFK��[�

x FRVK��[� \�� FRVK�[ FRVK�\� VLQK�[ VLQK�\�x FRVK��[� \�� FRVK�[ FRVK�\� VLQK�[ VLQK�\�x VLQK� �[� \�� VLQK�[ FRVK�\ � FRVK�[ VLQK�\�x VLQK� �[� \�� VLQK�[ FRVK�\ � FRVK�[ VLQK�\�x WDQK��[� \�� WDQK WDQKWDQK WDQK[ \[ \��� �x WDQK��[� \�� WDQK WDQKWDQK WDQK[ \[ \��� �x VLQK��[ � VLQK�[ FRVK�[�x FRVK��[ FRVK��[� VLQK��[ � FRVK�[� � � ��� � VLQK��[�x WDQK��[ �� �WDQKWDQK[ [� �

&RQWRK����� -LND�WDQ�I VLQK�[��_I_ � �� S��WXQMXNNDQ�EDKZD� GG[I VHFK�[�

Page 21: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���-DZDE���7XUXQDQ�GDUL�NHGXD�UXDV�SHUVDPDDQ�\DQJ�GLEHULNDQ�WHUKDGDS�[ DGDODK� �VHF FRVK� I IGG[ [ �.DUHQD�WDQ�I VLQK�[��PDND�VHF��I ��� WDQ��I ��� VLQK��[ FRVK��[��$NLEDWQ\DGG[ [ [[ [ [I I FRVKVHF FRVKFRVK FRVK� � � VHFK ��GDQ�WHUEXNWLODK�\DQJ�GLLQJLQNDQ���.DLWDQ�)XQJVL�+LSHUEROLN�GHQJDQ�+LSHUERO�6DWXDQ���.LWD�LQJDW�NHPEDOL�NDLWDQ�DQWDUDIXQJVL�WULJRQRPHWUL�GHQJDQ�OLQJNDUDQ�VDWXDQ��-LND�WLWLN�3�[� \��WHUOHWDN�SDGD�OLQJNDUDQ�VD�WXDQ�[� � \� ���PDND�[ FRV�W GDQ�\ VLQ�W PHPHQXKL�FRV��W � VLQ��W ���GDQ�OXDVVHNWRU� OLQJNDUDQ�\DQJ� GLEDQJXQ�ROHK�EXVXU� OLQJNDUDQ�GDUL� ������NH� �[� \�� DGDODK�/�W� �� W ��3DGD�*E�����OXDV�GDHUDK�\DQJ�GLDUVLU�DGDODK/�W�� W�S ��OXDV�OLQJNDUDQ� W�S ��S �� W �

\�[� � \� ������VLQ W

����������������������FRV W �������[��*E���

\VLQK�W

$ %������������������FRVK W

*E���6LWXDVL�\DQJ�VDPD�WHUMDGL�SDGD�*E�����-LND�WLWLN�3�[� \��WHUOHWDN�SDGD�KLSHUERO�VDWXDQ[� � \� ���PDND�[ FRVK�W GDQ�\ VLQK�W PHPHQXKL�FRVK��W � VLQK��W ���GDQ�OXDVVHNWRU�\DQJ�GLEDQJXQ�ROHK�EXVXU�KLSHUERO�GDUL�������NH��[� \��DGDODK�/�W�� �� W ��8QWXNNDVXV�W t ���NLWD�GDSDW�PHPEXNWLNDQQ\D�GHQJDQ�FDUD�VHEDJDL�EHULNXW�/�W�� /XDV�VHJLWLJD�2%3� OXDV�GDHUDK�$%3

�� �� �FRVK VLQK FRVKW W [ G[W� �³ �7HRUHPD�GDVDU�NDONXOXV�PHPEHULNDQ� �� �� �

c � � � � ! � / W W W W WW W W WW W� � FRVK VLQK FRVK �VLQKFRVK VLQK VLQK �FRVK VLQK � �

�� � � ��� � � ��� � � �� ��

�� �NDUHQD�

3�[� \� �FRV W� VLQ W�\ [ �� �

[

[� � \� �

3�[� \� �FRVK W� VLQK W�

Page 22: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���,QL�PHQJDNLEDWNDQ�/�W�� �� W � F��F NRQVWDQWD��.DUHQD�/��� ���PDND�F ���.DUHQD�LWX�/�W�� �� W ��W t ���8QWXN�NDVXV�W � ���IXQJVLQ\D\ [ � �� � GDQ��� FRVK VLQK VLQK� ��W W W� � �VHKLQJJD� GHQJDQ� SURVHV� GL� DWDV� DNDQ� GLSHUROHK� KDVLO� \DQJ� VDPD�� 'HQJDQ� GHPLNLDQWHUEXN�WLODK�\DQJ�GLLQJLQNDQ���,QYHUV� )XQJVL� +LSHUEROLN� � � ,QYHUV� IXQJVL� KLSHUEROLN� GLNRQVWUXNVL� GHQJDQ� FDUD� \DQJVDPD�VHSHUWL�LQYHUV�IXQJVL�WULJRQRPHWUL�x ,QYHUV�)XQJVL�6LQXV�+LSHUEROLN ,QYHUV�VLQXV�KLSHUEROLN��GLWXOLV�\ VLQK�� [��DWDX\ DUF�VLQK�[��DGDODK�IXQJVL�\DQJ�PHPHQXKL\ VLQK�� [ � [ VLQK�\��[� 5 GDQ�\� 5�x .DUHQD� VLQXV� KLSHUEROLN� GDSDW� GLQ\DWDNDQ� VHEDJDL� IXQJVL� HNVSRQHQ�� PDND� LQYHUVIXQJVL�VLQXV�KLSHUEROLN�GDSDW�GLQ\DWDNDQ�VHEDJDL�IXQJVL�ORJDULWPD�QDWXUDO��\DLWX

x VLQK�� [ OQ � �[ [� �� � ��[� 5�x 'DUL�[ VLQK�\ �� �H \ � H�\ ��GLSHUROHK��[ H \ � H�\��\DQJ�PHQJKDVLONDQ

x �H \��� � �[H \ � �� ��x 6HOHVDLNDQ�SHUVDPDDQ�NXDGUDW�GDODP�H \� LQL�GHQJDQ�UXPXV�DEF��GLSHUROHK

x H [ [ [ [\ r � r �� � �� �� � �x .DUHQD�H \ ! ���PDND� H [ [\ � �� � ��VHKLQJJD�\ VLQK�� [ OQ � �[ [� �� � �x ,QYHUV�)XQJVL�.RVLQXV�+LSHUEROLN ,QYHUV�NRVLQXV�KLSHUEROLN��GLWXOLV�\ FRVK�� [�DWDX�\ DUF�FRVK�[��DGDODK�IXQJVL�\DQJ�PHPHQXKL\ FRVK�� [ � [ FRVK�\��[t ��GDQ�\t ��x 'DODP�EHQWXN�ORJDULWPD�QDWXUDO��FRVK�� [ OQ � �[ [� �� � ��[t ��x ,QYHUV�)XQJVL�7DQJHQ�+LSHUEROLN ,QYHUV� WDQJHQ�KLSHUEROLN�� GLWXOLV�\ WDQK�� [�DWDX�\ DUF�WDQK�[��DGDODK�IXQJVL�\DQJ�PHPHQXKL\ WDQK�� [ � [ WDQK�\��_[_ � ��GDQ�\� 5�x 'DODP�EHQWXN�ORJDULWPD�QDWXUDO��WDQK�� [ �� OQ ����[[ ��_[_ � ��x ,QYHUV�)XQJVL�.RWDQJHQ�+LSHUEROLN ,QYHUV�NRWDQJHQ�KLSHUEROLN� GLWXOLV�\ FRWK��[��DWDX�\ DUF�FRWK�[��DGDODK�IXQJVL�\DQJ�PHPHQXKL\ FRWK�� [ � [ FRWK�\��_[_ ! ��GDQ�\� 5 � ^�`�x 'DODP�EHQWXN�ORJDULWPD�QDWXUDO��FRWK�� [ �� OQ [[���� ��_[_ ! ��

Page 23: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���x ,QYHUV�)XQJVL�6HNDQ�+LSHUEROLN ,QYHUV�VHNDQ�KLSHUEROLN��GLWXOLV�\ VHFK�� [��DWDX\ DUF�VHFK�[��DGDODK�IXQJVL�\DQJ�PHPHQXKL\ VHFK�� [ � [ VHFK�\����� [d ��GDQ�\t ��x 'DODP�EHQWXN�ORJDULWPD�QDWXUDO��VHFK�� [ OQ � � �� � [[ ����� [d ��x 'DUL�[ VHFK�\ �FRVK \ GLSHUROHK�FRVK�\ �[ ��\ t ���VHKLQJJD�\ FRVK�� �[ ��,QLPHQJDNLEDWNDQ

x VHFK�� [ FRVK�� �[ ��[t ��x ,QYHUV�)XQJVL�.RVHNDQ�+LSHUEROLN ,QYHUV�NRVHNDQ�KLSHUEROLN��GLWXOLV�\ FVFK�� [�DWDX�\ DUF�FVFK�[��DGDODK�IXQJVL�\DQJ�PHPHQXKL\ FVFK�� [ � [ FVFK�\��[z ��GDQ�\z ��x 'DODP�EHQWXN�ORJDULWPD�QDWXUDO��FVFK�� [ OQ � � �� �[[ ��[z ��x 'HQJDQ�FDUD�VHSHUWL�IXQJVL�VHNDQ�KLSHUEROLN��GLSHUROHK

x FVFK�� [ VLQK�� �[ ��[z ��*UDILN�IXQJVL�LQYHUV�KLSHUEROLN�GLSHUROHK�GHQJDQ�FDUD�PHQFHUPLQNDQ�JUDILN�IXQJVLKLSHUEROLN�WHUKDGDS�JDULV�\ [��KDVLOQ\D�GLSHUOLKDWNDQ�SDGD�*E�����*E�����GDQ�*E����\\ VLQK�� [\ FRVK�� [�� � [\ VLQK�� [

*E���

\\ FRWK�� [

����� ������������������[\ WDQK�� [

\ FRWK�� [*E���

\\ FVFK�� [

�������������������������[\ FVFK�� [

*E���7XUXQDQ�,QYHUV�)XQJVL�+LSHUEROLN���7XUXQDQ�LQYHUV�IXQJVL�KLSHUEROLN�GDSDW�GLSHUROHKGDUL�WXUXQDQ�EHQWXN�ORJDULWPD�QDWXUDOQ\D�DWDX�GHQJDQ�WXUXQDQ�IXQJVL�LQYHUV��KDVLOQ\D�GL�EHULNDQ�GDODP�WHRUHPD�EHULNXW�7HRUHPD��������7XUXQDQ�,QYHUV�)XQJVL�+LSHUEROLN�D� � �GG[ [ [FRVK� �� �� � ��[! �� �G� � �GG[ [ [FRWK� �� ��� ��_[_ ! ��

�� \ VHFK�� [

Page 24: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ����E� � �GG[ [ [VLQK� �� �� � ��[� 5��F� � �GG[ [ [WDQK� �� ��� ��_[_ � ��

�H��� � �GG[ [ [ [VHFK� ��� ��� ����� [� ���I ��� � �GG[ [ [ [FVFK� ��� ��� ��[z ��

%XNWL���.LWD�EXNWLNDQ�EDJLDQ��D��VDMD��VLVDQ\D�GLVHUDKNDQ�XQWXN�ODWLKDQ�SHPEDFD�'DUL�\ FRVK�� [ OQ � �[ [� �� � ��[t ��GLSHUROHK

� �� � � �c � � � �§©̈̈ ·¹̧̧

� � � �� � !\ G\G[ [ [ [[

[ [ [ [[ [ [� � � �

� � � � � � �� �

��

� �

�� � �

&DUD� ODLQ 'DUL� \ FRVK��� [ � [ FRVK \�� [ t �� GDQ� \ t ��� GDQ� G[G\ VLQK� \GLSHUROHK c � � !\ G\G[ G[G\ \ \ [ [� � � � � � �� �VLQK FRVK � �NDUHQD�VLQK�\t ��XQWXN�\t ����

%HULNXW�LQL�DGDODK�EHEHUDSD�FRQWRK�\DQJ�EHUNDLWDQ�GHQJDQ�LQYHUV�KLSHUEROLN�&RQWRK����� 7HQWXNDQ�WXUXQDQ�SHUWDPD�GDUL�IXQJVL�D��\ WDQK����VLQ��[��������GDQ��������E��\ VLQK����OQ�[��-DZDE %HUGDVDUNDQ�7HRUHPD������GDQ�DWXUDQ�UDQWDL�GLSHUROHK�KDVLO�EHULNXW��D� c � \ G\G[ [ [ [[ [ [�� � � � � �� �� � �� �VLQ �� FRV � FRVFRV FRV VHF ��E�� c � �\ G\G[ [ [ [ [� � � ��� �OQ � OQ �

&RQWRK����� -LND�WDQ�I VLQK�[��_I_ � �� S ��Q\DWDNDQ�[ GDODP�I GDQ�KLWXQJODK� G[GI �-DZDE���'DUL�WDQ�I VLQK�[��_I_ � �� S GLSHUROHK�[ VLQK�� �WDQ�I���%HUGDVDUNDQ�UX�PXV VLQK�� [ OQ � �[ [� �� � ��[�5��NLWD�PHPSXQ\DL

Page 25: 5-2 Fungsi Transenden

���,QWHJUDO�GDQ�)XQJVL�7UDQVHQGHQ ���� � � � � �[ � � ��VLQK WDQ OQ WDQ WDQ OQ WDQ VHF� � �I I I I I �'DUL�VLQL�GLSHUROHKG[GI I I II I I I II I I �� �� VHF VHF WDQWDQ VHF VHF �VHF WDQ �VHF WDQ VHF� �

NDUHQD�VHF�I � WDQ�I z ��XQWXN�_I_ � �� S ���������6RDO�/DWLKDQ8QWXN�VRDO���VDPSDL�GHQJDQ����EXNWLNDQ�VH�WLDS�NHVDPDDQ�\DQJ�GLEHULNDQ��� FRVK �FRVK ��� �� �[ [ � ��� VLQK �FRVK � �

�FRVK � �������

� �� �[ [ [

[ [ � !� � �­®°°̄ �

�� WDQK FRVKFRVK �FRVKFRVK ���

�� ��� �[ [[ [

[[ [ �� !� �� �­®°°°̄° �

�� WDQ VLQKFRVK FRVKVLQK�� � �[ [[ [ [ � � ��� WDQK � OQ �[ [[ ���� �� ��� �� ��� WDQKWDQK [[ H [ �

8QWXN� VRDO� �� VDPSDL� GHQJDQ� ���� WHQWXNDQWXUXQDQ�\c GDUL�VHWLDS�IXQJVL�\DQJ�GLEHULNDQ����\ VLQK��VLQ�� [����\ VLQK�� �VLQ�[��� \ �VLQ�[�WDQK�[����\ WDQK�� �H[ �����\ FVFK�� �WDQ�[�8QWXN�VRDO����VDPSDL�GHQJDQ�����WHQWXNDQWXUXQDQ�\c GDUL�EHQWXN�LPSOLVLW�\DQJ�GLEHULNDQ�����WDQK�[\ FRVK�\����OQ��VLQK�[�� FRVK�[\����WDQK�� [ OQ�[\����FRWK�� [\ WDQK��[ � \�����-LND�VHF�I FRVK�[�� I S� �� ��Q\DWDNDQ

[ GDODP�I GDQ�KLWXQJODK� G[GI �