- #1

Charismaztex

- 45

- 0

## Homework Statement

Evaluate the limit: [tex]lim_{(x)\rightarrow(2)}\frac{x^2+x-6}{sqrt(x+4)-sqrt(6)}[/tex]

## Homework Equations

N/A

## The Attempt at a Solution

I've drawn the graph which indicates that the at x=2, y=0, so 0 would seem to be the limit.

I could not, however, get the limit expression by algebraic manipulation to get to 0.

First of all, I rationalized the denominator to give x-2, which is a common factor of the numerator and the denominator. But canceling this, I am left with the expression:

[tex]lim_{(x)\rightarrow(2)}((x+3)(sqrt(x+4)+sqrt(6))[/tex]

after the [tex]lim_{(x)\rightarrow(2)}\frac{x-2}{x-2}[/tex] comes to 1.

I may have missed something crucial, so I just can't get the limit to be 0

Any help is greatly appreciated,

Charismaztex