Question

设f(x)在x0可导,则limΔx趋近0f(x0+Δx)的平方-f(x0)的平方/Δx等于

Answer 1

f(x)在x0处可导,则

Δx→0 时

lim [f(x0+Δx)-f(x0)]/Δx =f'(x0)

lim [f(x0+Δx)+f(x0)] = 2f(x0)

则

lim [ [f(x0+Δx)²-f(x0)²]/Δx

= lim [ [f(x0+Δx)+f(x0)][f(x0+Δx)-f(x0)]/Δx

= 2f(x0)f'(x0)