# Need help on limit problem

1. Jan 20, 2013

### Torshi

1. The problem statement, all variables and given/known data
Finding limit: involves trig

2. Relevant equations

Lim X-> 0 ((tan(x))^2 / X)

3. The attempt at a solution

I've done multiple other problems, but can't do this one, my trig is weak.

2. Jan 20, 2013

### SammyS

Staff Emeritus
Did you try L'Hôpital's rule ?

3. Jan 20, 2013

### Staff: Mentor

A well-known limit that can be used in this problem is this one:
$$\lim_{x \to 0} \frac{sin(x)}{x} = 1$$

4. Jan 20, 2013

### Torshi

We're not there yet in lecture. I just started College level calculus. We have so far just defined what limits are and using εδ def. of limits and I'm having a hard time understanding the rules for using epsilon and delta to prove an argument and some limit problem solving involving trig etc.

5. Jan 20, 2013

### Torshi

I know this and the other one is = 0. My prof said memorize it, but I don't know how to incorporate it. I feel like I'm in a rough start for calc...I'm not bad in math per se, I've taken college alg, statistics, physics 1/2, gen chem 1/2 etc all a year ago or more, haven't taken trig or precal. I took the math placement and scored enough somehow to end up in this hard class that i need.

6. Jan 20, 2013

### SammyS

Staff Emeritus
Write tan(x) in terms of sin(x) & cos(x) .

7. Jan 20, 2013

### Torshi

are you implying i should need to know the identities such as 1-cosx = sinx^2 for example - not that this has to do anything with the prob? Sorry if I'm off, but I never took trig

8. Jan 20, 2013

### Dick

You need to know tan(x)=sin(x)/cos(x). You do need to know a LITTLE trig.

9. Jan 20, 2013

### Staff: Mentor

It's actually cos2(x) = 1 - sin2(x).
That's something you'll need to rectify, since many of the problems you'll see will require some knowledge of basic trig identities. For starters, you need to be able to write tan(x), cot(x), sec(x), and csc(x) in terms of sin(x) and/or cos(x).

10. Jan 20, 2013

### Torshi

I still can't solve it. I know sin(x)/x = 1

edit: Alright, I'll brush up on my trig identities etc. But, this HW is due on Tuesday. I'll youtube how to do that

11. Jan 20, 2013

### Staff: Mentor

No, $lim_{x \to 0} \frac{sin(x)}{x} = 1$, but that's different from what you wrote.

12. Jan 20, 2013

### Torshi

So I have written down all the identities. Would (Tan(x)^2) which is the numerator first turn into Tan^2(x) which i believe is another way of writing it.

I also have down here that Tanθ = Sinθ / Cosθ.....................Also tan^2θ = Sec^2θ-1 ?

Edit: I did a similar problem and got it right. lim X--> 0 F(x) = 1-cosx / x

1.) 1-cosx / x multiplied by 1+cosx / 1+cosx
2.) 1^2 - cosx^2 / x (1+cosx) then becomes sin^2x / x(1+cosx)
3.) 1 x 0 = 0

Last edited: Jan 20, 2013
13. Jan 20, 2013

### Torshi

So far I'm assuming I have:

1.) tan^2x = Sec^2x - 1

2.) Sec^2x -1 / x X Sec^2x+1 / Sec^2+1

3.) Sec^4 -1 / x (sec^2x+1)

?? good so far?

edit: I think i'm doing it wrong

14. Jan 20, 2013

### haruspex

Go back to tan = sin/cos, sin(x)/x tends to 1 as x tends to zero. What do you think cos(x) tends to as x tends to 0?

15. Jan 20, 2013

### Torshi

I think the answer is zero I believe for my overall problem

16. Jan 20, 2013

### haruspex

Yes, but why?

17. Jan 20, 2013

### Torshi

I don't know I'm so confused, this crap has been bugging me all day. It's been a while since I've done all this.

All my prof said was that lim x-->0 sinx/x = 1 and lim x-->0 1-cosx/x = 0 . This is calc so he just assumes we know it, he didn't review any precalc or trig obv. He just speeds right through.

I wrote down all the trig identities such as tanx=sinx/cosx etc etc and cos^2x + sin^2x =1

I know these things are all related. In one of my posts I figured out an answer due to trig identities. I can't for this one... I'm sure it's very simple, I just can't see it.

I don't see how I can relate (tan(x)^2)/x to any of them...

18. Jan 20, 2013

### Dick

Yes, it is. Can you explain why?

19. Jan 20, 2013

### Dick

tan(x)^2/x=(sin(x)/x)*(sin(x)/cos(x)^2). What's the limit of each of those two factors?

20. Jan 20, 2013

### haruspex

That had better be lim x-->0 (1-cosx)/x = 0 .
Do you know what cos(0) is? Given that, and knowing that sin(x)/x -> 0, and sin(x) = cos(x)tan(x), what can you say about lim x->0 tan(x)/x?