Question

Find the following limit algebraically:

Answer 1

\[\lim_{x \rightarrow 2}\frac{ \sin(x ^{2}-4) }{ (x ^{2}-4) }\]

Answer 2

I don't see how to cancel sin, even after multiplying by (x^2+4) / (x^2+4)

Answer 3

Limit is 1

Answer 4

I know it's 1

Answer 5

This is a 0/0 form

Answer 6

So you see that if it's a 0/0 form then sinx/x tends to 1

Answer 7

I know, but I still have to show the work.

Answer 8

Simply write that since it is easily visible that it's a 0/0 form and sinx/x limit is 1.

Answer 9

If you know L'hospitals rule?

Answer 10

You may show by that way too!