1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Limits of fractions of polynomials and trig functions

  1. Sep 25, 2007 #1
    I have two...

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


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


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


    3. The attempt at a solution
    I plugged in the 3, and got 3/0, then I got lost...
     
  2. jcsd
  3. Sep 25, 2007 #2

    EnumaElish

    User Avatar
    Science Advisor
    Homework Helper

    In 2, did you try simplifying the numerator? (What are the roots of the polynomial?)
     
  4. Sep 26, 2007 #3
    Yes, I tried doing that.

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

    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?
     
  5. Sep 26, 2007 #4

    EnumaElish

    User Avatar
    Science Advisor
    Homework Helper

    What is a short hand expression for (x-3)(x-3)?
     
  6. Sep 26, 2007 #5
    (x-3}^2. Oh yeah, so that takes away the square root, and after everything, it leaves 0. thank you.
     
  7. Sep 26, 2007 #6

    Avodyne

    User Avatar
    Science Advisor

    In the first one, are you sure the problem isn't x->0 instead of x->1 ?
     
  8. Sep 26, 2007 #7
    it is 1, not 0.
     
  9. Sep 26, 2007 #8

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Well, then your book has a typo..
     
  10. Sep 26, 2007 #9
    it's not from my book, it was my teacher.
     
  11. Sep 26, 2007 #10

    Avodyne

    User Avatar
    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.
     
  12. Sep 26, 2007 #11

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    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.
     
  13. Sep 26, 2007 #12
    allright, thankyou.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Limits of fractions of polynomials and trig functions
  1. Limit of trig function (Replies: 23)

Loading...