设f(x)在x=2处可导,且f'(2)=1,则lim h→0 [ f(2+h)-f(2-h)]/h等于多少,
问题描述：
设f(x)在x=2处可导,且f'(2)=1,则lim h→0 [ f(2+h)-f(2-h)]/h等于多少,
答
由导数的定义可知f(x)在x=2处可导,且f'(2)=1，就是说lim h→0，f(2+h)/h=1
[ f(2+h)-f(2-h)]/h
= f(2+h)/h-f(2-h)/h
=f(2+h)/h+f【2+(-h)】/（-h）
=1+1=2
答
lim (h→0) [ f(2+h)-f(2-h)]/h
=lim (h→0) f(2+h)/h-lim (h→0)f(2-h)]/h
=lim (h→0) f(2+h)/h+lim (h→0)f(2-h)]/(-h)
=f'(2)+f'(2)
=2
答
由导数的定义可知f(x)在x=2处可导,且f'(2)=1,就是说lim
于是,lim [ f(2+h)-f(2-h)]/h
= lim [ f(2+h)-f(2)+f(2)-f(2-h)]/h
=lim (f(2+h)-f(2))/h+(f(2-h)-f(2))/(-h)
=f'(2)+f'(2)
=1+1
=2