www.MasterMathMentor.com Stu Schwartz A.P. Calculus - ln and e Practice test 1) y = ln !14 x 3 ( ) 2) y = ln 2 x ( ) 5 3) y = ln 4 ! x 2 ( ) 4) y = ln (ln (cos x)) 5) y = x 4 1 ! 2 ln x 6) y = ln x 2 + 1 x 2 ! 1 4 7) y = e !4x+ 4 8) y = 2e 2x 3 9) y = xe 2 ! e x 10) y = 4 2x !1 11) y = ! x x ! 12) x 4 + e xy ! y 2 = 20
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www.MasterMathMentor.com Stu Schwartz
A.P. Calculus - ln and e Practice test 1)
y = ln !14x
3( ) 2) y = ln 2x( )
5
3)
y = ln 4 ! x 2( ) 4) y = ln (ln (cos x))
5) y =
x 4
1! 2 ln x 6)
y = ln
x2 +1
x2 !1
4
7) y = e
!4x+ 4 8) y = 2e2x
3 9)
y = xe2
!ex 10)
y = 42x !1
11) y = !
xx! 12) x
4+ e
xy! y
2= 20
www.MasterMathMentor.com Stu Schwartz
Find the integral or definite integral as indicated
13)
1
5 - x ! dx 14)
7x dx
x2 ! 8
"
15)
8x3 ! 7x
2 !1
2x" dx 16)
x2 ! 5x + 2
x ! 2" dx
17)
(ln x)3
2x ! dx 18)
(e
4x+ e) ! dx
19)
2ex(1+ e
x)
4 ! dx 20)
ex
+ e-x
ex ! e
! x " dx
21)
(e
x- e
-x)
2 ! dx 22)
!e
cos x sin x " dx
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23)
ex
2 x1
4
! dx 24)
2
x1
e2
! dx
25) Find relative extrema and inflection points of y = xe
! x Use calculus methods and be sure that your work is understandable.
26) Given f x( ) = e
x2
a) Find the area of the region R bounded by the line y = e, the graph of f and the y-axis.
b) Find the volume of the solid generated by revolving R about the x-axis.