Homework Help: Simple Limit of a Trigonmetric Function

1. Apr 4, 2009

waterbugirl

1. The problem statement, all variables and given/known data

Find the limit algebraically.
lim x--> 0 sin (x)/3x

2. Relevant equations

lim x--> 0 (sin x)/x = 1

3. The attempt at a solution
I tried multiplying both sides by (3/3) and got and answer of (1/3).
But if I multiply sin (x) by 3, is that the same thing as sin (3x) ?

Last edited: Apr 4, 2009
2. Apr 4, 2009

rl.bhat

But if I multiply sin (x) by 3, is that the same thing as sin (3x) ?

No. In that case the answer would be 1, which is wrong.

3. Apr 5, 2009

waterbugirl

Okay, so how do I do it?

4. Apr 5, 2009

kbaumen

if you know that

$$\lim_{x\rightarrow 0} \frac{\sin(x)}{x} = 1$$

but given is

$$\lim_{x\rightarrow 0} \frac{\sin(x)}{3x}$$

you, probably, have to rearrange the given expression to turn it or a part of the given expression into the form of the formula. How would you do that?

5. Apr 5, 2009

n!kofeyn

You had a right idea here, but executed it a little wrong. To get from $\sin x/x$ to $\sin x/(3x)$ you don't multiply by 3/3. You multiply/divide by...

Also, there is also the property that if $\lim_{x\to a} f(x)$ exists, then
$$\lim_{x\to a} \left[ cf(x) \right] = c \lim_{x\to a} f(x)$$