# Limits of fractions of polynomials and trig functions

by carbz
Tags: limits, solved
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 P: 35 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...
 Sci Advisor HW Helper P: 2,481 In 2, did you try simplifying the numerator? (What are the roots of the polynomial?)
 P: 35 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?
 Sci Advisor HW Helper P: 2,481 Limits of fractions of polynomials and trig functions What is a short hand expression for (x-3)(x-3)?
 P: 35 (x-3}^2. Oh yeah, so that takes away the square root, and after everything, it leaves 0. thank you.
 Sci Advisor P: 1,200 In the first one, are you sure the problem isn't x->0 instead of x->1 ?
 P: 35 it is 1, not 0.
 Sci Advisor HW Helper PF Gold P: 12,016 Well, then your book has a typo..
 P: 35 it's not from my book, it was my teacher.
 Sci Advisor P: 1,200 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.
 Sci Advisor HW Helper PF Gold P: 12,016 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.
 P: 35 allright, thankyou.

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