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!

Another math test question

  1. Oct 7, 2011 #1
    1. The problem statement, all variables and given/known data
    i think I remember the question to be this:

    lim (y-3)/(y-3)(y+3)
    y→3

    it was the first limit question and the easiest but im not sure if I did it right.

    2. Relevant equations



    3. The attempt at a solution

    so what I did was I cancelled the y-3's out to get:

    1/(y+3) and this is what I was unsure about is that the first step and after this I got:


    1/(3+3) = 1/6
     
  2. jcsd
  3. Oct 7, 2011 #2
    You're correct:

    [tex]

    \lim_{y \to \ 3} \frac{y-3}{(y-3)(y+3)} = \lim_{y \to \ 3 } \frac{1}{y+3} = \frac{1}{6}

    [/tex]
     
  4. Oct 7, 2011 #3
    You have the correct answer, but it's probably a good idea to try to justify your last step. When is it true that [itex] \lim_{y \to a} f(y) = f(a) [/itex]? What can you say about the continuity of rational functions?
     
  5. Oct 7, 2011 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    A crucial, and often overlooked property of limits is this: if f(x)= g(x) for all x except x= a, then [itex]\limit_{x\to a} f(x)= \limit_{x\to a}g(x)[/itex].

    For this problem, you can correctly say that
    [tex]\frac{y-3}{(y-3)(y+3)}= \frac{1}{y+3}[/tex]
    for all x except x= 3 and so the limits are the same.

    Actually, "what can you say about the continuity of rational functions?" is NOT a good question here because continuity also involves the value of the function as well as the limit. 1/(x+3) is continuous at x= 3, so its limit is 1/(3+3)= 1/6 while (x-3)/(x-3)(x+3) is NOT continuous at x= 3.
     
  6. Oct 7, 2011 #5
    This statement is true exactly because rational functions are continuous anywhere their denominator isn't zero, which is why I asked the question. I guess I should have mentioned the fact that there is a removable singularity at x=3, but the OP seemed to handle it appropriately.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Another math test question
  1. Maths question (Replies: 2)

  2. Math questions (Replies: 2)

Loading...