anonymous one year ago How to find the limit of sin(x)/x as x approaches zero? For example, the problem is sin (2x)/ 8x, how to find the limit as x approaches to zero?

1. anonymous

will it be 1/4 since the limit of sin(x)/x is equal to 1?

2. anonymous

We know that $\lim_{x \rightarrow 0} \frac{\sin x}{x} = 1$ Looking at the given problem $\lim_{x \rightarrow 0} \frac{\sin 2x}{8x}$ In order to get the problem to look like the form sin x / x, we need the denominator of the fraction to equal 2x. Setting the bottom to 2x, the limit looks like this: $n \ \lim_{x \rightarrow 0} \frac{\sin 2x}{2x}$ In order for the above to be true, we would have to multiply the limit by some number $$n$$. That's what you have to find.

3. anonymous

Yeah, it works out to be 1/4.

4. anonymous

ah okay thanks! one more question, why is it that $$\lim_{x \rightarrow 0} \frac{\sin x}{x} = 1$$ ? Is there a proof that it is equal to 1?

5. anonymous

I just know about it but I never learned the reason behind it