# Homework Help: Limits involving cosine

1. Feb 22, 2012

### mtayab1994

1. The problem statement, all variables and given/known data
find the limit of :

$$\lim_{x\rightarrow0}\frac{\sqrt{5-cos(x)}-2}{x^{2}}$$

2. Relevant equations

3. The attempt at a solution

I multiplied the numerator and the denominator by the conjugate of the numerator and i got :

$$\frac{1-cos(x)}{x^{2}(\sqrt{5-cos(x)}+2)}$$

then: i divided top and bottom by x^2 and i got (1/2)/4 which is 1/8.

Is what I have done correct?

Last edited: Feb 22, 2012
2. Feb 22, 2012

### tiny-tim

hi mtayab1994!
oooh, i've never seen that trick before! :tongue2:

yes, that's fine

(the usual way of dealing with cosx is to replace it by 1 - x2/2 … same result)

3. Feb 22, 2012

### mtayab1994

Yea thanks. And by the way I didn't know that you replace cos x with 1-x^2/2. Well maybe it's because we haven't done it yet.

4. Feb 22, 2012

### tiny-tim

ah!

yes, cos x = 1 - x2/2 + x4/4! - x6/6! + …