# Solving limits with trig. functions

1. Jul 22, 2010

### mybrainhurts1

Can anyone help me with these two limit problems...
solve:

lim h->o (h^2-h+sinh)/2h

and

lim y->0 (sin3cot5y)/ycot4y

I know lim x->0 sinx/x=1, but I cant figure out how to get these two into that format.

Last edited: Jul 22, 2010
2. Jul 22, 2010

### Staff: Mentor

Split it up into the sum of three separate limits.
Typo here? Should this be lim y->0 (sin3ycot5y)/ycot4y?
If so, split it up into the product of three separate limits, after working with cot5y and cot4y.

3. Jul 22, 2010

### mybrainhurts1

Yes, should be lim y->0 (sin3ycot5y)/ycot4y

So for the first problem--
(h^2/1)-(h/2)+sinh/h= (0^2/1)-(0/2)+1=1...?

4. Jul 22, 2010

### Staff: Mentor

No.
First, you omitted the fact that a limit is involved.
Second, you have multiple algebra errors.

5. Jul 22, 2010

### mybrainhurts1

6. Jul 22, 2010

### Staff: Mentor

Are you able to find the errors in the first problem?

7. Jul 22, 2010

### mybrainhurts1

limx->o h^2/2h - limx->0 h/2h + limx->0 sinh/2h, but where do I go from here.

8. Jul 22, 2010

### Staff: Mentor

$$\lim_{h \to 0} \frac{h^2}{2h} = (1/2) \lim_{h \to 0} h * \frac{h}{h}=(1/2) \lim_{h \to 0} h * \lim_{h \to 0}\frac{h}{h}$$

It's valid to move constants in or out of the limit, and it's valid to split up limits into sums or products of limits, as long as the individual limits exist.

Can you continue from here for this limit and the other two?