Simple Limit of a Trigonmetric Function

[waterbugirl]

Homework Statement

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

Homework Equations

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

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) ?

 

[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.

 

[waterbugirl]

Okay, so how do I do it?

 

[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?

 

[n!kofeyn]

Homework Statement

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) ?

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
$$\lim_{x\to a} \left[ cf(x) \right] = c \lim_{x\to a} f(x)$$