Question

How do you find the limit of `(sqrt(x+4) -2) / x` as x approaches 0?

Answer 1

`1/4`

Explanation:

We have limit of indeterminate form, ie `0/0` so can use L'Hopital's rule:

`lim_(xrarr0) (sqrt(x+4) - 2)/x = lim_(xrarr0)(d/(dx)(sqrt(x+4)-2))/(d/(dx)(x))`

`=lim_(xrarr0)(1/(2sqrt(x+4)))/1 = 1/(2sqrt(0+4)) = 1/4`