Question

How do you find the derivative of `f(x) = x+3` using the limit definition?

Answer 1

`f'(x) = 1`

Explanation:

Applying the limit definition of the derivative , we have:

`f'(x) = lim_(h->0)(f(x+h)-f(x))/h`

`=lim_(h->0)((x+h+3)-(x+3))/h`

`=lim_(h->0)h/h`

`=lim_(h->0)1`

`=1`