Question

Question #80354

Answer 1

I found: `1/(2sqrt(3))`

Explanation:

If you try direct,y you get:
`lim_(x->3)(sqrt(x)-sqrt(3))/(x-3)=0/0`
Which is an indeterminate form (we cannot solve `0/0`).
So to try to avoid this we can try using De l'Hospital Rule deriving top and bottom and then apply the limit:

`lim_(x->3)(1/(2sqrtx))/1`

As `x->3`:

`lim_(x->3)(1/(2sqrt(x)))=1/(2sqrt(3)`