Question

Find the limit (Picture Provided)

Answer 1

`a. \: 4`

Step-by-step explanation

Given:

`f(x) = {x}^(2)`

`f(2) = 4`

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

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

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

Substitute;

`lim_(h\to 0) \frac{ {h}^(2) + 4h + 4 - 4}{h}`

`lim_(h\to 0) \frac{ {h}^(2) + 4h }{h}`

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

Plug in zero,

`= 0 + 4`

`= 4`