Question

Find the limit
Picture below

Answer 1

a. 4

Explanation:

We want to find;

`\lim_(h \to 0) (f(2+h)-f(2))/(h)`

If
`f(x)=x^2`.

`f(2+h)=(2+h)^2`

`f(2+h)=4+4h+h^2`

Also;

`f(2)=2^2`

`f(2)=4`

This implies that;

`\lim_(h \to 0) (4+4h+h^2-4)/(h)`

Simplify;

`\lim_(h \to 0) (4h+h^2)/(h)`

Factor to get;

`\lim_(h \to 0) (h(4+h))/(h)`

Cancel the common factors.

`\lim_(h \to 0) 4+h`

Substitute h=0 to get

`\lim_(h \to 0) 4+h=4+0=4`