# Trig Limit Question

1. Oct 13, 2011

### batman2002

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

Find the limit as x approaches ∏/8, (cos(2x)-√(2))/(x-∏/8)

2. Relevant equations

cos(2x)+cos(2a)

3. The attempt at a solution

I tried to multiply the conjugate of the terms but ended up stuck there, don't know how to go on. Please help.

2. Oct 13, 2011

### Staff: Mentor

This isn't an equation, and I don't see how it's relevant to anything.
As x approaches $\pi$/8, what does the numerator approach? What does the denominator approach?

3. Oct 13, 2011

### batman2002

You end up with -(1/sqrt2)/0 limit. the equation is an identity that is supposed to help when solving the question.

I also tried expanding the relevant equation and ended up with, cos(2x)+cos(2a)=-2sin(x+a)sin(x-a)

4. Oct 13, 2011

### Staff: Mentor

cos(2x)+cos(2a) is NOT an equation, so it can't possibly be an identity.
But that's not a number. I agree that the numerator approaches -1/sqrt(2), which is the same as -sqrt(2)/2. And I agree that the denominator approaches 0.

So this problem is similar to these limits:

$$\lim_{x \to 0}\frac{1}{x}$$
$$\lim_{x \to 0}\frac{1}{x^2}$$

How would you characterize these two? (One of them has a direct bearing on your limit.)

5. Oct 13, 2011

### batman2002

I am not exactly sure about that.

6. Oct 13, 2011

### Staff: Mentor

What is it that you're not exactly sure about? If you think that cos(2x)+cos(2a) is an identity, I am absolutely certain that you are wrong.

Are you unsure that your limit is related to one of the ones I gave, you can start by answering my question.