Question

Limits

Answer 1

\[\lim_{x \rightarrow -\infty}\frac{ 4x }{ \sqrt{3+x^2} }\]

Answer 2

Have you learnt the l'hopital rule?

Answer 3

We might have gone over it, but I can't recall it

Answer 4

Do it analytically is possible too.

As x becomes very large, the 3 is insignificant and can be ignored. Simplify this:\[\Large \frac{ 4x }{ \sqrt{x^2} }\]

Answer 5

It'll simplify to:\[\Large \frac{ 4x }{ \left| x \right| }\]which means if it's x is negative...

Answer 6

Alright, I have it up to here. Where do I go form here?

Answer 7

Just simplify. If you can't do it as is, imagine if x=-1, or something like that. You'll see it's very easy.

Answer 8

\[\frac{ 4(-1) }{ \left| -1 \right| }\]

-4?

Answer 9

exactly

Answer 10

Alright, well thanks a lot!

Answer 11

no problem