# A limit problem

1. Sep 23, 2006

### ocean09

hi guys,

I need help w/ finding the limit for the following problem:

t-->9

t-->0
Another question, how do you guys do those

2. Sep 23, 2006

### LeonhardEuler

I'm not sure I understand the question. Is the first one:
$$\lim_{t\rightarrow 9} 9-\frac{t}{3} -\sqrt{t}$$?
If so, this is not difficult because it is the sum of three continuous functions.
For the second, is it:
$$\lim_{x\rightarrow 0} x^2-\frac{81}{\sqrt{x}}-3$$?
If so, then this is also not difficult since the limits of the first and last terms are finite while that of the middle term is not. (I'm assuming that 't' in the second one is supposed to be an 'x'. If not then I don't understand.)

To see how to make these math symbols, click on them.

3. Sep 23, 2006

### Data

probably safer to assume the limits he wants are

$$\lim_{t \rightarrow 9} \frac{9-t}{3-\sqrt{t}}$$

and

$$\lim_{x \rightarrow 0} \frac{x^2-81}{\sqrt{x}-3}.$$

The second one is continuous at 0 so you can just sub x=0 in. Are you sure it's not $x \rightarrow 9$ again?

For the first one, you can factor it. I'll let you try for yourself first.

4. Sep 23, 2006

### ocean09

You are correct.

oops. That was a typo. it's x-->9

Factor? I thought I'm supposed to multiply top and bottom by radical x -3...correct me if I'm wrong...

This might be a stupid question.

How do you guys show your work like that? Is there a special program?

Thanks.

Last edited: Sep 23, 2006