Find the limit as x->0 of (2-2cos(x))/(sin(5x))

Question

Mathematically I got 2/5, but on the graph it appears to be 0.

Answer 1

Not sure how you got 2/5, but I got 0 as well.

Here's what I did:

Lim x->0 (2-2cos(x))/sin(5x)
both numerator and denominator evaluate to zero, so we can use d'Hôpital's rule:
=Lim x->0 (0+2sin(x))/5cos(5x)
This new expression evaluates to 0/5=0, which is therefore the answer.

Answer 2

Thanks. I made a really stupid error. You've been very helpful in answering my calc questions. I really appreciate it.

Answer 3

You're very welcome.
Keep up the good work. Calculus is best learned with lots of practice.