[SOLVED] Limits

carbz

I have two...

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


2. Relevant equations
[latex]\lim_{x \rightarrow 1} \frac{1-cosx}{x^2}[/latex]


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
[latex]\lim_{x \rightarrow 3} \frac{\sqrt{x^2-6x+9}}{x-3}[/latex]


3. The attempt at a solution
I plugged in the 3, and got 3/0, then I got lost...

EnumaElish

In 2, did you try simplifying the numerator? (What are the roots of the polynomial?)

carbz

Yes, I tried doing that.

[latex](x-3)(x-3)[/latex]

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?

EnumaElish

What is a short hand expression for (x-3)(x-3)?

carbz

(x-3}^2. Oh yeah, so that takes away the square root, and after everything, it leaves 0. thank you.

Avodyne

In the first one, are you sure the problem isn't x->0 instead of x->1 ?

carbz

it is 1, not 0.

arildno

Well, then your book has a typo..

carbz

it's not from my book, it was my teacher.

Avodyne

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.

arildno

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.

carbz

allright, thankyou.