高数求救 设f '(x)存在,h→0时,lim (f(x+2h)-f(x-3h))/h
问题描述：
高数求救 设f '(x)存在,h→0时,lim (f(x+2h)-f(x-3h))/h
答
△x=(x+2h)-(x-3h)=5h
lim (f(x+2h)-f(x-3h))/h
=lim (f(x+2h)-f(x-3h))/(5h)*(1/5)
=5f'(x)
答
lim (f(x+2h)-f(x-3h))/h =5f'(x)
答
f'(x)的定义是lim(h→0) [f(x+h)-f(x)]/h =f'(x)所以lim (f(x+2h)-f(x-3h))/h=lim [(f(x+2h)-f(x))+(f(x)-f(x-3h))]/h=lim [f(x+2h)-f(x)]/2h*2+[f(x)-f(x-3h)]/(3h)*(3)=2f'(x)+3f'(x)=5f'(x)
答
lim (f(x+2h)-f(x-3h))/h
=lim (f(x+2h)-f(x)+f(x)-f(x-3h))/h
=5f'(x)