# Homework Help: Why does this limit equal 1?

1. May 6, 2013

### YYaaSSeeRR

I have a question and here it is :

[(1/e^x)-1] / [(1/e^x)+1]

why this equal -1 ?? when X →±∞

I would appreciate it if you explain it for me on a paper after you capture it by your camera.

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2. May 6, 2013

### Infrared

Are you sure the answer is 1? The limit should be -1.

3. May 6, 2013

### YYaaSSeeRR

sorry I forgot to put the - , yea it does equal -1 but why?

4. May 6, 2013

### Infrared

What is $$\lim_{x\rightarrow \infty} {e^{-x}-1}?$$
$$\lim_{x\rightarrow \infty} {e^{-x}+1} ?$$ Just divide these two answers.

5. May 6, 2013

### micromass

That only works for the limit to $+\infty$.

6. May 6, 2013

### YYaaSSeeRR

yes and that drives me crazy

7. May 6, 2013

### Infrared

Thanks, fixed.

For negative x, multiply the numerator and denominator by $e^x$

8. May 6, 2013

### YYaaSSeeRR

so what about when x→-∞ ?

9. May 6, 2013

### micromass

First things first. Do you understand the limit when $x\rightarrow +\infty$?

10. May 6, 2013

### YYaaSSeeRR

yes I do.

11. May 6, 2013

### micromass

Cool. For the other limit, you'll need to follow the hint in #7.

The answer won't be -1, by the way.

12. May 6, 2013

### YYaaSSeeRR

I have not seen this after the modification :)

thanks a lot ,this problem forced me to throw the book away.

13. May 6, 2013

### micromass

So you found the right answer??

Also: you might want to post this in "calculus and beyond" next time :tongue2:

14. May 6, 2013

### YYaaSSeeRR

yes I got the right answer.

you must see teachers here in Syria ,they drive you crazy.
can't wait till I graduate high school and arrive to the US.

15. May 7, 2013

### YYaaSSeeRR

actually when I followed hint #7 the answer wasn't -1 ,so Micromass what is the right answer?

16. May 7, 2013

### ChaseRLewis

(e^-x - 1) / (e^-x +1)

Multiply num and denom by e^x

(1 - e^x) / (1 + e^x)

so ya if you got positive 1 with negative infinite that makes sense as that reduces to
1/1 = 1

17. May 7, 2013

### YYaaSSeeRR

(1 - e^x) / (1 + e^x) when x→-∞

yea it does equal 1 , but in my textbook when x→-∞ the equation (e^-x - 1) / (e^-x +1) equal -1 and that make no sense for me.

18. May 7, 2013

### micromass

19. May 7, 2013

### HallsofIvy

Are we still talking about "[(1/e^x)-1] / [(1/e^x)+1]" as x goes to infinity? For very large x, 1/e^x is very close to 0 so the fraction is close to -1/1= -1.

(Oh, I see. The original post said "as $x \to \pm\infty$" and the limit as x goes to negative infinity is 1.)

20. May 7, 2013

### micromass

No, we're talking about the limit to $-\infty$.