1. ## Limits involving trig

2. Originally Posted by janedoe
They multiplied by 1/2 and divided by 1/2.

In the last step they used the fact that $\frac{sin x}{x}$ goes to 1 and x goes to 0.

3. Originally Posted by apcalculus
They multiplied by 1/2 and divided by 1/2.

In the last step they used the fact that $\frac{sin x}{x}$ goes to 1 and x goes to 0.

I'm sorry, I'm still not getting it =[ You mean, multiply the whole thing by 1/2, and then divide vy half as in, multiply by 2/1 ?

4. Originally Posted by janedoe
I'm sorry, I'm still not getting it =[ You mean, multiply the whole thing by 1/2, and then divide vy half as in, multiply by 2/1 ?

If you have a fraction like $\frac{m}{n}$ , it is the same as

$\frac{1*m}{0.5*\frac{n}{0.5}}$

Now split into a product of fractions and write the 0.5 and $\frac{1}{2}$, to get:

$\frac{1}{\frac{1}{2}} \frac{m}{\frac{n}{\frac{1}{2}}}$

Note that $\frac{1}{\frac{1}{2}}$ is 2 and can be pulled in front of the limit sign since it is a constant.

That's all we're doing. I hope this helps.