[SOLVED] Limits

I have two...

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

2. Relevant equations
$\lim_{x \rightarrow 1} \frac{1-cosx}{x^2}$

3. The attempt at a solution
I figured to just plug in 1, but I wanted to make sure....

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

2. Relevant equations
$\lim_{x \rightarrow 3} \frac{\sqrt{x^2-6x+9}}{x-3}$

3. The attempt at a solution
I plugged in the 3, and got 3/0, then I got lost...
 PhysOrg.com science news on PhysOrg.com >> King Richard III found in 'untidy lozenge-shaped grave'>> Google Drive sports new view and scan enhancements>> Researcher admits mistakes in stem cell study
 Recognitions: Homework Help Science Advisor In 2, did you try simplifying the numerator? (What are the roots of the polynomial?)
 Yes, I tried doing that. $(x-3)(x-3)$ However, I forgot how to get rid of that radical. Squaring wouldn't work, so I have no idea. Also, no thoughts on the first one?

Recognitions:
Homework Help

[SOLVED] Limits

What is a short hand expression for (x-3)(x-3)?
 (x-3}^2. Oh yeah, so that takes away the square root, and after everything, it leaves 0. thank you.
 Recognitions: Science Advisor In the first one, are you sure the problem isn't x->0 instead of x->1 ?
 it is 1, not 0.
 Recognitions: Gold Member Homework Help Science Advisor Well, then your book has a typo..
 it's not from my book, it was my teacher.
 Recognitions: Science Advisor Well, it's 99% certain that your teacher meant to write 0 instead of 1. With 1, it's trivial, since both the numerator and denominator are finite, nonzero constants in that limit.
 Recognitions: Gold Member Homework Help Science Advisor Then he either blundered, or tried to fool you. Your function is defined&continuous on all values of x except x=0. Your original approach is perfetly valid in the case of x=1.
 allright, thankyou.