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Question Number 162539 by LEKOUMA last updated on 30/Dec/21
Calculate lim_(h→0) ((f(3−h)−f(3))/(2h)), with f′(3)=2
Calculatelimh→0f(3−h)−f(3)2h,withf′(3)=2
Answered by Ar Brandon last updated on 30/Dec/21
lim_(h→0) ((f(3−h)−f(3))/(2h))=(0/0) →LH =lim_(h→0) ((−f ′(3−h))/2)=((−f ′(3))/2)=−1
limh→0f(3−h)−f(3)2h=00→LH=limh→0−f′(3−h)2=−f′(3)2=−1
Answered by mr W last updated on 30/Dec/21
lim_(h→0) ((f(3−h)−f(3))/(2h)) =−(1/2)lim_(h→0) ((f(3−h)−f(3))/((−h))) =−(1/2)lim_(Δx→0) ((f(3+Δx)−f(3))/(Δx)) =−(1/2)f′(3) =−(1/2)×2 =−1
limh→0f(3−h)−f(3)2h=−12limh→0f(3−h)−f(3)(−h)=−12limΔx→0f(3+Δx)−f(3)Δx=−12f′(3)=−12×2=−1

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