"
f(x) = x cos(x - 1) (1, f(1))
sin x
f(x) = (0, f(0))
" x
x
f(x) = x (0, f(0))
"+
f(x) = ln x + 1 (0, f(0))
f(x) = (-x2) (1, f(1))
" "
f(x) = x2 + 1 - 2 x0 = 3
x2
f(x) = (1, f(1))
2x " "
f(x) = (1 + x)ln x (1, y0)
"
3
y = x2, y = x
y = 3-x
"
(x0, 3)
"
3x
f(x) = - 1
f(x) = 3 - x2
Ą
3
x
2
f(x) = x
a b f(x) = -x2 + ax + b
y = x (-1, -1)
f(x) = 4 - x
x2
g(x) = 4 -
2
"
3
sin 211o 0, 999 7, 999 e0,04
1
"
cos 209o 31,98 ln (0, 999)
3,98
3
ą
"
3
f(x) = x x0 = 8 R4
f(x) = ln(1 + x) x0 = 0 R3
f(x) = cos x x0 = Ą R6
 ln(1, 2) 10-3
"
10-2
sin 3o 10-4
10-3
"
f(x) = 1 + x R5
"
2
f(x) = sin2 x R4
sin2 1
5
"
n
f(x) = 1 + x R4
3 3
2
" x
5
1 + x H" 1 + 0 < x d" 0, 1
5
"
x x2
1 + x H" 1 + - 0 d" x d" 1,
2 8
x3 Ą
sin x H" x - |x| <
6 6
ex + 2x = 1, 03 x7 + 4x5 + 3x3 + 2x = 9, 9962 x + ln x = 3, 71
2x - cos x = 3, 14 x2011 + 2011x = 2010 xx = 28
"
3
f(x) = x2 + 1 [-1, 1]
f(x) = |x - 1| [0, 2]
1
f(x) = [0, 3]
1 + x
f(x) = arccos x [-1, 1]
x 1
arcsin " = arccos " x " [0, +")
1 + x2 1 + x2
1 2x
arctgx = arctg x " (-1, 1)
2 1 - x2
Ą
arctgx + arcctgx = x " R
2
x
"
arcsin x = arctg x " (-1, 1)
1 - x2
"
sin(arccos x) = 1 - x2 x " (-1, 1).
x
< ln(1 + x) < x x > 0
x + 1
ex > 1 + x x > 0
x
x d" arcsin x d" " x " 0, 1)
1 - x2
a
ln d" b - a 1 d" a d" b
b
 ex > ex x > 1
-x
f(x) = x2
f(x) = arctgx - ln x
f : R - R
f (x) > 0 x " (", 1) *" (4, ") f (x) < 0 x " (1, 4) f (1) f (4)
1
f (x) > 0 x " (", 1) f (x) < 0 x " (1, ") f-(1) = 1 f+(1) = - f(1) = 2
2