# Help with trig limit

• Nov 16th 2009, 02:32 PM
paupsers
Help with trig limit
Can anyone show me how the limit of $\frac{sin 5x}{x}$ as x goes to 0 equals 5?

I'm only supposed to use the fact that $\frac{sin x}{x}$ goes to 1 as x goes to 0.

Any tips?
• Nov 16th 2009, 02:37 PM
Drexel28
Quote:

Originally Posted by paupsers
Can anyone show me how the limit of $\frac{sin 5x}{x}$ as x goes to 0 equals 5?

I'm only supposed to use the fact that $\frac{sin x}{x}$ goes to 1 as x goes to 0.

Any tips?

If we let $z=5x$ then our limit becomes $\lim_{z\to0}\frac{\sin(z)}{\tfrac{z}{5}}$........so