# X^2 limit help

1. Oct 3, 2007

### skateza

1. The problem statement, all variables and given/known data
lim as x approaches 1 from the left of (sin$$(\sqrt{1-x})$$)/$$\sqrt{1-x2}$$

and

lim as x approaches infinity $$(x^{2}+sinx)/(x^{2}+cosx)$$

3. The attempt at a solution
I have attempted to solve these although my brain is raw, i have done a hundred limits today because my assignment is due tomorrow and im just lost on these ones... any starting tips

Last edited: Oct 3, 2007
2. Oct 3, 2007

### Dick

The second one is easy. sin and cos are bounded. x^2 isn't. Your first problem doesn't have enough parentheses in it to make it clear. But in any event, since it looks like it is of a 0/0 form I would use L'Hopital's rule. Is it sin of the whole thing or just of the first sqrt. And does x2 mean 2*x or x^2?

Last edited: Oct 3, 2007
3. Oct 3, 2007

### skateza

ok i fixed the parentheses,

What do u mean by sin and cos are bounded

4. Oct 3, 2007

### Dick

I mean |sin(x)|<=1 and same for cos while x^2 goes to infinity. Now does x2 mean x^2 or 2*x?

5. Oct 3, 2007

### skateza

sorry, yeah it means x^2

6. Oct 3, 2007

### Dick

I'm still going for trying to hit the first one with L'Hopital's rule. How's the second one going?

7. Oct 3, 2007

### Hurkyl

Staff Emeritus
Isn't the first one just sin x / x in disguise?

8. Oct 3, 2007

### Dick

Sure it could be done that way. I'm still waiting for the OP to do SOMETHING. The second one is not that hard.

9. Oct 3, 2007

### skateza

I've solved the second one, i got 1, easy... just divided by the highest power of x in the denom. I did it a while ago i just for got to post sorry haha.... but the first one has still got me,, because their is an x^2 in the bottom, so its not quite sinx/x

10. Oct 3, 2007

### Dick

You can factor (1-x^2)=(1-x)*(1+x). I was wondering if I had lost you.

11. Oct 4, 2007

### skateza

perfect solved it, 1/root2

12. Oct 4, 2007

Yes you did.