Mat Demo Standart 20...2 $ - 3 3 î ù ñ ó ï þ î å ý ü î ø ö î û î ù å õ ò ü ð å ò ø ü ð å ú î ó þ å î ù ö ý # 3 " ! $ 3 4 3 - $ - % * % # " ! $
Post on 11-Sep-2020
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1.2.
3.
4.5.
1.
2.
4.
5.
6.
.
1
2
0
400234
2 3 4324
2304
a2 b2 = (a b a + b(a + b 2 = a2 + 2ab + b2
(a b 2 = a2 ab + b2
ax2 + bx + c a 0D = b2 ac
x = –b D—2a x2 = –b + D—2a D 0
x = x2 = –b—2 D = 0 ax2 + bx + c = a(x x x x2
a = n = a a an
a R n N n 2
a0 0 a2 =
a–n = —n n N
am—n = amn m Z n N n 2
ax ay = ax + y x
—y = ax – y (ax y = ax y
(ab x = ax bx (ab
x =
x—bx
a b c k 0
alogab = b log
log (b c b + log c
log bc = log b c
log bn = n log b
log k b = k log b
an = a + d(n Sn = a + n—2 n
Pn 2 3 n = n! C kn = n!—k! (n k A k
n = n!—(n kP (A = kn
bn = b qn Sn = b (qn—q (q
a = a –a 0
1.
200150100
350300250
500
2.
3
3
3.
4. 2
5. MBA o
M B C
A D?
25o
o o o o o
4
o
A
M25o
6. y = f(x
( a 2 + a
2 2 4 2
8. F F C
o
oF oF oF oF oF
y
y = f(x)
x1–1 410
oF
F
2
110
y = = f((ff x)x
(2x2 3—4x
2—x3
2—x4
4—x3
3—2x4 —2x
11.x y
x + 4y = x0; y0 x0 y0
4 3
xx +xx0
—2
12. f(x x3 + tgx
f (x x2 + —tg x
f (x x —tg x
f (x x4 + —cos2 x
f (x x2 + —cos2 x
f (x x4 —tg x
13. x
+ + +
14. o
2 23—2
3—22—2
o
15.
2 3 4
16.
CNB DM i DN
o MBND
2 2 2 2 2
M N
A C
D
B
BNDDM
2
--
123
y = 2x
y xy x
y
x1–3 310
y
x1–3 310
y
x1–3 310
x –3311 33
18. =
123
1 a2
2 a3 log2 (4 + a
3
123
1 2 3
CB K
DA
D
123
12 C3
A1
B1 C1
D1
A D
CB
A
B
D1
21.
1.
2.
22. ACB o
1.
O15o
A
C
B
C
O5o
23.
1.
2. AC
C
24. an a2 a4
1.
2. S20
25.
26.
y = x 1.
x y0
0
2. y = x 3.
4. F(x f (x x 5. S
f 6. S
xf (ff xxS
28. SABCD ABCD
1. SABCD SA
SABCD
CDBC
( = 0 x
( x = 2 x (ex = ex
(ln x = x (sin x = cos x
(cos x = sin x (tg x = cos2x
(u + v = u + v (u v = u v
(uv = u v + uv (Cu = Cu
(u–v = u v uvv2
sin = y cos = x sin2 + cos2
tg = 2 = cos2
sin2 = 2sin cos cos2 = cos2 sin2 o = cos o = sin o = sin o = cos
o = tg o = tg
a
b
f(x dx = F(x a
b = F(b F(a
0–1
–1
1
1
y
x
M(x , y )
x
y
tg
cos
sin
0o0
0
0 0 0
30o
2
2
2—2
—3
2—2
3—23—2
o4
3
o3
o o o o2
3—2 2
0
0
0
0
F(x CC
f(x
0 C
x — + C
ln x + C
x + C
sin x x + Ccos x sin x + C
tg x + C—cos2 x
ex ex + Cx
x
o
o
s
os2
sin
tg
in
cos
2
s2
a = F(FF b
—cos2
cos x
ex
x
C
20
S = ab sinS = aha
V = S HS = P H
V = 3 S H
S = 2 P m
V = R2H
S = 2 RH
V = 3 R2H
S = RL
V = 43 R3
S = 4 R2
L = 2 R
(x x02 + (y y0
2 = R2S = R2
S = 2 d d2
d d2 S = a + b—2 h
a b S = ab
p = a + b + c—2 + +
a2 = b2 + c2 bc cosa— = b—sin = c—sin = 2R
R – ABC
a2 + b2 = c2
bc = cos ac = sin a
b = tg
c
ab
C
A B
ha
ca
b
a
b ha
a
bd1
d2
a
b
h
R
M(x0, y0)
H
M(x0, y0, z0)
A(x1, y1, z1) B(x2, y2, z2)
H m H
R
RH L
R
R
S = 2a ha S = 2b c S = p(p a p b p c
x0 = x + x2—2 y0 = y + y2—2 z0 = z + z2—2
AB (x2 x y2 y z2 z AB (x2 x 2 + (y2 y 2 + (z2 z 2
a b = a b + a2b2 + a3b3
a b = a b
a(a1, a2, a3)b(b1, b2, b3)
H
x y2 y
)
M y0
V = 3S
H
R
d2
S = 2 d d
d2
c
n
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