"
sin(5x+1)
f(x) = xn, g(x) = ln(2x + 5), h(x) = 3x - 1, i(x) = sin ln(5x + 1) , j(x) = ,
"
k(x) = ln( x), l(x) = sin2 3x.
x2
x- x
-1 ax-bx 1-x ln x 1 1
"
lim , lim , lim , lim (Ą - 2 x) ln x, lim , lim , lim - ,
x3 x0 cos x-1 ln x ln sin x x2 sin2 x
x 1-x2 x"
x0 x0 x1 x0 x0
1
1
x2 sin
x- x
1 1
x
x2
lim , lim x - x2 ln 1 + , lim xsin x, lim x - , lim x2 , lim ( x)2x-Ą , lim ,
x2 x x x Ą sin x
x0 x" x0 x0 x0 x0
x
2
1
1
sin x
x-sin x 1 ln cos x x
x
"ln x x
lim , lim , lim (1 - x) ln(1 - x), lim x , lim , lim , lim (1 + ) .
x"
x1+ x2-1 x0 x3 x1- x0+ x x0 ln cos 3x x"
1 1
-
sin x 1 2 x2
x-2
" x2
f(x) = 6x + , g(x) = x , h(x) = , i(x) = x + - 3, j(x) = , k(x) = ,
x (x-2)2 x
x2-2
1
x2+3x-2 x3
x-4
l(x) = x - x, m(x) = x x, n(x) = , o(x) = x , p(x) = .
x2-4 x-1
x2
x x3 -2x
x-3
f(x) = , g(x) = x - ln(1 + x), h(x) = x - , i(x) = , j(x) = x2 , k(x) = x3 + 2x2 - 8,
x-1
"
(x+2)2 3
x x
l(x) = 1+ (x-1), m(x) = , n(x) = x3-10x2+24x, o(x) = , p(x) = 3-2 x2, q(x) = ,
ln x (x+1)3 ln x
"
1
x2 8
x
r(x) = x2 , s(x) = x 4 - x2, t(x) = + .
2 x2
1
f(x) = x2 +
x2
1-x
f(x) = [0, 1],
1+x
f(x) = 2x3 - 3x2 - 36x - 8 [-3, 6],
x
f(x) = (x - 3)2 [-1, 4],
"
f(x) = x + 2 x [0, 4],
f(x) = xx [0, 3].
"
x2 1 x 1
f(x) = , g(x) = , h(x) = x, i(x) = , j(x) = ln x + , k(x) = x 1 - x2,
x2+1 1-x2 ln x
-x 1
l(x) = x2 , m(x) = x3 - 6x2 - 36x + 30, n(x) = x2 + , o(x) = x x, p(x) = x2 ln x,
x
1 1 sin 2x
r(x) = ln x - , s(x) = , t(x) = 2 sin x + , u(x) = x3 ln x + 1.
ln x x 2
1
3x-1 x 1 x -x
x
f(x) = , g(x) = , h(x) = x , i(x) = , j(x) = , k(x) = x , l(x) = sin x - sin2 x,
2x+1 x2+1 ln x ln x
" "
x2(x-1)
x 1
m(x) = x 1 - x2, n(x) = x2 , o(x) = , p(x) = , q(x) = ln x + x2 + 1 ,
x (x+1)2
2x x4 ln 1 x3
"x
r(x) = , s(x) = , t(x) = , u(x) = ln + , v(x) = , w(x) = x + 2 x.
1+x2 2-x3 x x (x-1)2