Finding Limits of Trig Functions

1. Aug 24, 2011

cheerspens

1. The problem statement, all variables and given/known data
The first problem I'm having difficulty with is

$\stackrel{lim}{x\rightarrow0}$ $\frac{sin x}{5x}$

And the second is:
$\stackrel{lim}{x\rightarrow0}$ $\frac{sin x(1-cos x)}{2x^{2}}$

2. Relevant equations
I assume that for the first problem I need to simplify it to the rule where $\stackrel{lim}{x\rightarrow0}$ $\frac{sin x}{x}$=1
and the second would probably need to simplify to follow the rule $\stackrel{lim}{x\rightarrow0}$ $\frac{1-cos x}{x}$=0

3. The attempt at a solution
What I mainly need help with is how to get started. For the first problem, how do I get rid of the 5x at the bottom?
For the second problem should I square the entire thing and end up with $\stackrel{lim}{x\rightarrow0}$ $\frac{2sin x}{4x^{4}}$ then go from there or is that even correct?

2. Aug 24, 2011

rock.freak667

Rewrite the first one as (1/5)(sinx/x) then take the limit.

use the fact that x2=x*x and then try to get sinx/x and (1-cosx)/x then use the fact that lim(x→a) f*g = lim(x→a) f * lim(x→a) g

3. Aug 25, 2011

rude man

Use the power series for sin(x) and cos(x).