The limit lim (h->0) of (sqrt(81+h)-9)/h represents the derivative of some function f(x) at some number a. Find f and a

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`lim_(h-gt0) (sqrt(81+h) - 9 )/ h`

`` Let f(x)= sqrtx

==> The limit represent the function`f(x) = sqrt(x)`

`` Now, the limit represent the derivative at a by the definition.

`==gt lim_(h-gt0) (f(a+h)-f(a))/h`

 

`` `==gt lim_(h-gt0) = (sqrt(a+h) - sqrt(a))/h`

Now , comparing both limits, we notice that `sqrta = 9 `

`` `==gt a = 9^2 = 81`

`==> f(x)= sqrtx and a= 81`

 

``

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