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!

Limit of ln(sinx)

  1. Sep 1, 2011 #1
    1. The problem statement, all variables and given/known data
    [itex]lim_{x \to 0+} ln(sin(x))[/itex]

    [itex]lim_{x \to \infty} [ln(1+x^2)-ln(1+x)][/itex]

    2. Relevant equations


    3. The attempt at a solution
    I'm really not sure how to take this limit at all?

    I know (from using a table) that it tends towards -infinity, but I am not sure how to go about taking it manually?

    I am thinking that because as x approaches 0, sin(x) approaches 0, you can treat sin(x) like x. Then as x approaches 0, ln(x) approaches -infinity.

    For the second one, if I separate it into two limits, they both go towards infinity, then it's infinity - infinity?
     
    Last edited: Sep 1, 2011
  2. jcsd
  3. Sep 1, 2011 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Intuitively, that is correct. You can make it rigorous with a δ, ε argument. If you can use the fact that ln(x) → -∞ as x → 0+ then you know that given any N > 0 there is a δ > 0 such that ln(x) < -N if 0 < x < δ. Now put that together with a similar type of argument about sin(x), knowing that sin(x) → 0 as x → 0.
     
  4. Sep 1, 2011 #3

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    For the first one, I think the most rigorous approach (besides epsilon-delta) is the squeeze theorem. Use

    [tex]\sin(x)\leq x[/tex]

    Take logs and take the limit.

    For the second one, first make one logarithm using

    [tex]ln(a/b)=ln(a)-ln(b)[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Limit of ln(sinx)
  1. Limit ln (Replies: 1)

  2. Limits of sinx/x (Replies: 7)

  3. Ln limit (Replies: 3)

Loading...