Question

How do you find the limit of `(3x^2+6x)/(x^2-4)` as x approaches 2?

Answer 1

Please see below !

Explanation:

`3x^2+6x=3x(x+2)`

`x^2-4=(x-2)(x+2)`

`(3xcancel((x+2)))/((x-2)cancel((x+2)))`

`(3x)/(x-2)`

I think you have Wrote the question wrongly and it approaches to `(-2)` instead

Or if it as you said approaches to 2 So, the answer is D.N.E (doesn't exist

look at the graph

the limit for the 2 from the left is `-oo` and from right `oo`

SO IT DOEN't exist.

graph{(3x^2+x6)/(x^2-4) [-8.38, 11.62, -9.28, 0.72]} )

BUT if it is approaches to -2 it gice you a value (`(3x)/(x-2)`) BLug in here,