\lim_(x\to \ 4) (x-4)/(√(x)-√(4) ) Please answer this one

Question

`\lim_(x\to \ 4) (x-4)/(√(x)-√(4) )` Please answer this one

Answer 1

`\large \boxed{\sf \ \ \lim_(x\to \ 4) (x-4)/(√(x)-√(4) )=4 \ \ }`

Explanation:

Hello,

We need to find the following limit.

`\displaystyle \lim_(x\to \ 4) (x-4)/(√(x)-√(4) )`

First of all, for any x real number different from 4 and positive, we can write

`(x-4)/(√(x)-√(4)) = \frac{(x-4)(√(x)+√(4))} {(√(x)-√(4))(√(x)+√(4))}} ==((x-4)(√(x)+√(4)))/(x-4)=√(x)+√(4)`

so the limit is

`√(4)+√(4)=2+2=4`

Hope this helps.

Do not hesitate if you need further explanation.

Thank you