find solution of the question of up pgt mathematics previous years question paper

Question : Find solution of the question of up pgt mathematics previous years question paperSolution :By the given expression \[limit_{h\rightarrow0}\frac{f\left(c+h\right)+f\left(c-h\right)-2f\left(c\right)}{h}\] we shall write this as \[=limit_{h\rightarrow0}\frac{f\left(c+h\right)-f(c)+f\left(c-h\right)-f(c)}{h}\] which becomes \[=limit_{h\rightarrow0}\frac{f\left(c+h\right)-f(c)}{h}-limit_{h\rightarrow0}\frac{f\left(c-h\right)-f(c)}{-h}\] that is \[=f^\prime\left(c+0\right)-f^\prime\left(c-0\right)\] Since f’(c) exists and non-zero, therefore \[f^\prime\left(c+0\right)=f^\prime\left(c-0\right)\] Therefore…

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