Let f (x) = x2, limx->; 2 f(x)-f(2)/x-2=？

limx-& gt； Infinite quintic limit (2x-1) 3 (x2+2) 2/(1-2x).

1, f(x) =x3 Find d[f(e minus x)=?

f(e^-x)=(e^-x)3=e^(-3x)

df=-3e^(-3x)dx

2. let f (x) = x2, limx->; 2 f(x)-f(2)/x-2=？

lim [f(x)-f(2)]/(x-2)

x→2

=lim [x2-22]/(x-2)

x→2

=lim (x-2)(x+2)/(x-2)

x→2

=lim (x+2)

x→2

=2+2

=4

3. limx- > infinite quintic limit (2x-1) 3 (x2+2) 2/(1-2x).

lim(2x- 1)3×(x2+2)2/[( 1-2x)3×( 1-2x)2]

x→∞

= lim[(2x- 1)/( 1-2x)]3×[(x2+2)/( 1-2x)]2

x→∞

= lim[(2- 1/x)/( 1/x-2)]3×[( 1+2/x2)/( 1/x2-2/x)]2

x→∞

=[(2-0)/(0-2)]×[( 1+0)/(-0)]

=- 1×(-∞)

=+∞

Description:

When x→∞, x2 is the high-order infinity of x.

1/x2 is the higher order infinitesimal of1/x.

1/x2- 1/x & lt； 0