Question

I don't know how to do limits with squareroots. Can someone help me? limit as x approaches zero of...

Answer 1

So you're trying to find\[\lim_{n\to0}\frac{\sqrt{4+n}-2}{n}.\]You can't just plug in 0 since we get an indeterminate form of \(\frac00\). To fix this problem, we're going to multiply by 1, but we're going to write it in a clever way. Let's multiply by\[\frac{\sqrt{4+n}+2}{\sqrt{4+n}+2}.\]What is\[(\sqrt{4+n}-2)(\sqrt{4+n}+2)?\]

Answer 2

1?

Answer 3

1/4

Answer 4

No. Try using the FOIL method.

Answer 5

okay so I multiply the two together without placing the zero in yet right?

Answer 6

Correct. Don't put the 0 in there yet.