Question

How do you find the limit of `(5x)/sqrt(x+2)` as `x->7`?

Answer 1

`lim_(x->7) (5x)/sqrt(x+2) =35/3`

Explanation:

`f(x)` is a rational function and as such it is continuous for every `x` in its domain. As the function is defined for `x=7` so, by definition of continuity, its limit equals its value:

`lim_(x->7) (5x)/sqrt(x+2) = [(5x)/sqrt(x+2)]_(x=7) = (5*7)/sqrt(7+2) =35/sqrt(9) =35/3`