"
f(x) = x2 f(x) = 2x + 5
"
3
f(x) = x f(x) = tg 2x
1
f(x) = ln(5x + 1) f(x) =
x + 3
"
f(x) = ln(2x + 5) f(x) = tg 3x - 1
sin(2x-3)
f(x) = sin ln(5x + 1) f(x) =
"
f(x) = ln( x) f(x) = sin2 3x
ex
f(x) = sin x + 2tgx - 2x - 3arctgx f(x) =
log x
1
" "
7
f(x) = x3 sin x f(y) = y + y + y +
"
3
y
"
2x + 1
f(x) = 2x + 5 f(x) =
x2
f(x) = tg 2x f(x) = ln(5x + 1)
f(x) = ln(x2 + 3x) f(x) = ln(2x + 5)
" "
f(x) = tg 3x - 1 f(t) = t 1 - t2
"
sin(2x-3)
f(x) = f(x) = ln( x)
f(x) = sin2 3x f(y) = arctg(2y - 3)
y
f(x) = sin (sin(cos x)) f(y) =
3 - y2
f(x) = logx(x + 1) f(t) = ett2 cos t
" "
1
h(x) = f(y) = y + 1 - ln(1 + y + 1)
tg2x
x x x
f(x) = tg - ctg f(x) = ln tg
2 3 2
"
1 + 1 - t2
f(x) = sin ln(5x + 1) f(t) = 3 ln
t
2
"
f(t) = et cos t f(x) = arcsinx-1
x
" "
4
f(x) = ctg x h(x) = arccos x
"
f(x) = xsin x f(x) = x + 1 - x2
1 1 - sin x
f(y) = arcsin f(x) = ln
y 1 + sin x
sin z2 "
3
x
f(z) = tg e4z f(x) = x
ln z
"
arcsinx 1 1 - 1 - x2 "
f(x) = " + ln " f(x) = sin [cos2 (tg3 ctgx)]
1 - x2 2 1 + 1 - x2
tg2t
f(y) = (sin y)ln y f(t) = sin3 t
"
4
f(x) = x + 1 + 2x + 1 f(x) = x(sin x)tgx
f(x) = arctgx f(x) = x3ex
" sin 2x
2
f(x) = xe-2x f(x) =
x3
n
1
f(x) = f(x) = sin x
x
x -2x
f(x) = x f(x) =
"
5
x x
lim lim
x" x"
2x ln x
"
x ln x
lim lim
x1
x0+ arcsin 2x x2 + x - 2
Ą - arctgx x - x
lim lim
x-" - arctg3x x3
x0
Ą
x2
- 1 3x - 2x
lim lim "
x0 - 1
x0
cos x
x 1 - x2
1 - x
lim (Ą - 2 x) ln x lim
x" x1
ln x
ln x 1 1
lim lim -
x0 x0
ln sin x x2 sin2 x
x - x
lim lim xsin x
x0 x0
x2 x
1
1
x2
lim x - lim x2
x0 x0
x
1
x2 sin
x
lim ( x)2x-Ą lim
Ą
x0
x sin x
2
ln x x - sin x
lim " lim
x0
x1+ x3
x2 - 1
1
x
lim (1 - x) ln(1 - x) lim x
x"
x1-
sin x
1 ln cos x
lim lim
x0
x0+ x ln cos 3x
1
1 1
x
x
lim (1 + ) lim -
x" x0
x sin x
1
x2
1 1 arcsin x
lim - lim
x1 x0
ln x x - 1 x
x2
2
lim arctgx lim [ln(x + 1)]x
x" x0
Ą
ex - e-x - 2x 1
lim lim x - x2 ln 1 +
x0 - sin x x
x"
x
xx - 1 x - sin x
lim lim
x1 x0 - tgx
ln x x
1
x2 sin
x - sin2 x
x
lim lim
x" x0
x + sin2 x sin x
1
x3 sin
x + sin x
x
lim lim
x" - sin x sin2 x
x0
x
x + cos 2x
lim
x-" - cos 4x
x