設函數fx在點x處可導,求下列極限.limf(x+αh)-f(x-βh)/h,(α,β均是常數)

設函數fx在點x處可導,求下列極限.limf(x+αh)-f(x-βh)/h,(α,β均是常數)


lim(h→0)[f(x+αh)-f(x-βh)]/h = lim(h→0)[f(x+αh)-f(x)]/h + lim(h→0)[f(x)-f(x-βh)]/h =α*lim(h→0)[f(x+αh)-f(x)]/(αh)+β*lim(h→0)[f(x-βh)-f(x)]/(-βh)=α*f'(x)+β* f'(x)=…