1. ## Limit Problem

(sqrt7-x)/(49-x^4) as x approaches sqrt7

I multiplied by the conjugate to rationalize the numerator. I also factored the bottom... and I came up with this.

(7-x)/(x^2+7)(x^2-7)

What to do after this?

2. $\lim_{x \to \sqrt{7}} \frac{\sqrt{7} - x}{49-x^4}$

$= \lim_{x \to \sqrt{7}} \frac{\sqrt{7} - x}{{\color{red}(7-x^2)}(7+x^2)}$

Try applying the difference of squares formula to the red

3. haha so obvious... sometimes I don't see these things. Thank you sir!

4. Originally Posted by Sturm88
Hey I have a really silly question, but what is a root + a root. like sqrt7 + sqrt 7 in the problem I just posted...
$a + a = 2a$. This is obvious right?

Imagine $a = \sqrt{7}$

5. So the answer is 28sqrt7?

6. (1/64)-(1/x^2)/(x-8) as x approaches 8

I used difference of squares on the top and I got this

(1/8x+x)(1/8-x)/(x-8) stuck here.