# Evaluating a limit: e^tan x

1. Oct 14, 2008

### phil ess

1. The problem statement, all variables and given/known data

Evaluate the following limit. lim as x approaches Pi/2 + of etan x.

2. Relevant equations

None.

3. The attempt at a solution

Well I've graphed this and I know it approaches 0, but I don't know how to actually solve this. And I'm fairly sure I'm not allowed to just substitute a number close to Pi/2, unless thats the only way. Thanks!

2. Oct 14, 2008

### =Lawrence=

The limit is zero. Actually, you can go to the table on your calculator (2nd, graph) and type in numbers that are extremely close and that will work. The limit is what it approaches, in this case from the right, and it's 0.

3. Oct 14, 2008

### Dick

The limit of tan(x) as x decreases to pi/2 is -infinity. To show that tan(x)=sin(x)/cos(x) and you probably know their limit around pi/2. Or just look at a graph of tan(x). Then just look at a graph of e^x as x->-infinity.

4. Oct 14, 2008

### =Lawrence=

Are you disagreeing with me? I can't tell what point you're trying to get across.

The limit of e^tan(x) as x approaches pi/2 from the right is zero.

5. Oct 14, 2008

### Dick

No, I'm agreeing with you. I'm just trying to say how to describe the problem without a calculator.

6. Oct 15, 2008

### phil ess

Ok thanks. I already knew the answer, and I can explain it conceptually. I just thought there was a more, mathematical?, way of showing the answer.

7. Oct 15, 2008

### Dick

You can do epsilons and deltas if you want. I don't think that's necessary.

8. Oct 15, 2008

### BoundByAxioms

Here is an informal way to think about it. The limit as x approaches pi/2+ of tan(x)= -infinity. e^(-infinity) = 1/(e^infinity) = 0.

9. Oct 15, 2008

### HallsofIvy

Staff Emeritus
ex and tan(x) are both continuous functions. $tan(\pi/2)= 0$ and e0= 1. Drum roll.

10. Oct 15, 2008

### Dick

tan(pi/2)=0??? tan(x) continuous??????