Question

设f(x)在x=a处可导,f'(x)=b 求极限lim(h-0) f(a-h)-f(a+2h)/ h

RT

Answer 1

lim [h→0] [f(a-h)-f(a+2h)]/h
=lim [h→0] [f(a-h)-f(a)+f(a)-f(a+2h)]/h
=lim [h→0] [f(a-h)-f(a)]/h + lim [h→0] [f(a)-f(a+2h)]/h
=-lim [h→0] [f(a-h)-f(a)]/(-h) - 2lim [h→0] [f(a+2h)-f(a)]/(2h)
=-f '(a)-2f '(a)
=-3f '(a)
=-3b

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