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Question Number 126824 by MathSh last updated on 24/Dec/20

$$\underset{x\to 2}{lim}\frac{f(x+2)-6}{x-2}=4if,\underset{x\to 4}{lim}\frac{4\cdot f\left(x\right)-24}{x-4}=?$$

Answered by mahdipoor last updated on 24/Dec/20

$$\underset{x\to 2}{lim}\frac{f(x+2)-6}{x-2}=\frac{f\left(4\right)-6}{0}=4\Rightarrow f\left(4\right)-6=0$$$$\stackrel{L^{\prime }hopital}{\Rightarrow }\underset{x\to 2}{lim}\frac{f(x+2)-6}{x-2}=\frac{f{}^{\prime }(x+2)}{1}=f{}^{\prime }\left(4\right)=4$$$$\underset{x\to 4}{lim}\frac{4\cdot f\left(x\right)-24}{x-4}=\frac{0}{0}\stackrel{L^{\prime }hopital}{\Rightarrow }\frac{4\times f{}^{\prime }\left(x\right)}{1}=4\times f{}^{\prime }\left(4\right)=16$$

Commented by MathSh last updated on 24/Dec/20

$$Sir,f^{\prime }\left(4\right)=4$$$$4\cdot 4=16$$

Commented by mahdipoor last updated on 24/Dec/20

$$oh!youareright$$$$thankfortip$$

Commented by MathSh last updated on 24/Dec/20

$$ThankyouSir,forhelpingthe$$

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