Another Limit question, problem in comments.

Question

anonymous · Answer

$$\lim_{x \rightarrow 4}(x-4)/(\sqrt{x}-2)$$

I've multiplied by the conjugate, and noticed there is a difference of squares on the top. However, I think I'm getting thrown off by the root x in the denominator.

myininaya · Answer

factor the top :)

myininaya · Answer

$$x-4=(\sqrt{x}-2)(\sqrt{x}+2)$$

myininaya · Answer

but the way you are talking about should also work

myininaya · Answer

$$\lim_{x \rightarrow 4}\frac{x-4}{\sqrt{x}-2} \cdot \frac{\sqrt{x}+2}{\sqrt{x}+2}=\lim_{x \rightarrow 4}\frac{(x-4)(\sqrt{x}+2)}{x-4}$$

anonymous · Answer

I'm blind. I was multiplying numerator and denominator by (x+4), as opposed to the Root x +2. No wonder I was going in circles. Thank you once again, myininaya.

anonymous · Answer

I feel like I should be paying you as a tutor :P

myininaya · Answer

lol you're so sweet