# Limits of trig functions

1. Jan 22, 2014

### Dan350

1.
what would be the limit?? with out using the L'Hopital's rule

lim_(x-0) (sin(3 x^2))/(8 x)

the limit of sin(3x^2) divided by 8x as x approaches zero

2. Limits of trignometric functions

3. The attempt at a solution
I tried factoring out the 1/8, but thats it, Idk how to go on

Hope you can help me

Thanks

2. Jan 22, 2014

### Dick

What's lim x->0 of sin(3x^2)/(3x^2)? That should be a good hint.

Last edited: Jan 22, 2014
3. Jan 22, 2014

### Dan350

1

but how to put the 3x^2 below?

4. Jan 22, 2014

### Curious3141

What (expression) do you have to multiply 8x by to get 3x2? As long as you multiply both the top and bottom by the same, you don't change the fraction.

5. Jan 22, 2014

### Dan350

3x on both numerator and denominator?
i would get 24x^2, but i can split the fraction right?

6. Jan 22, 2014

### Curious3141

So you get $\frac{3x\sin(3x^2)}{8(3x^2)}$. What happens next?

7. Jan 22, 2014

### Dan350

We factor out.

then the limx-0 of 3x/8 and limx-0 of sin(3x^2)/3x^2
therefore

limx-0 0*1
so

limx-0f(x)= 0

8. Jan 22, 2014

### Curious3141

Yes, exactly.