Results 1 to 7 of 7

Math Help - How to deal with undefined limits?

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    30

    How to deal with undefined limits?

    \text{For}\displaystyle  \lim_{x \to \infty} \frac{\sin{x}}{x}=\lim_{x \to \infty} \frac{1}{x}\times \lim_{x \to \infty} \sin{x}=0 \times \text{Unknown}

    Is the answer zero?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by crossbone View Post
    \text{For}\displaystyle  \lim_{x \to \infty} \frac{\sin{x}}{x}=\lim_{x \to \infty} \frac{1}{x}\times \lim_{x \to \infty} \sin{x}=0 \times \text{Unknown}

    Is the answer zero?
    -1\ \le\ sinx\ \le\ 1

    \displaystyle\lim_{x \to \infty}\ \left(-\frac{1}{x}\right)\ \le\ \lim_{x \to \infty}\frac{sin\;x}{x}\ \le\ \lim_{x \to \infty}\left(\frac{1}{x}\right)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2010
    Posts
    30
    Thanks! just curious, what's the answer to \displaystyle \lim_{x \to \infty} sin\;x \ ? Undefined?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,610
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by crossbone View Post
    Thanks! just curious, what's the answer to \displaystyle \lim_{x \to \infty} sin\;x \ ? Undefined?
    Yes that limit is not defined.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jan 2010
    Posts
    30
    Thanks! btw, what are indeterminate forms as far as limits is concern?
     \frac{0}{0}, \frac{\infty}{\infty}, \frac{0}{\infty}, \frac{\infty}{0}, \infty \times 0?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by crossbone View Post
    Thanks! just curious, what's the answer to \displaystyle \lim_{x \to \infty} sin\;x \ ? Undefined?
    Can you apply the squeeze theorem to \displaystyle\lim_{x \to \infty}\frac{sin\;x}{x}\;\;?



    Edit: sorry, the absence of a denominator bypassed my vision!
    Thanks Plato
    (next post).
    Last edited by Archie Meade; January 3rd 2011 at 01:19 PM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,610
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by Archie Meade View Post
    Can you apply the squeeze theorem to \displaystyle\lim_{x \to \infty}\sin(x)?
    Not to that limit. It bounces from -1 to 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: June 14th 2011, 02:36 PM
  2. FTC2 - Not sure how to deal with this one
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 31st 2011, 08:18 PM
  3. How to deal with the summation?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 24th 2011, 04:13 AM
  4. How do i deal with fractions when using Modulo?
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: February 11th 2011, 01:25 PM
  5. help! how to deal with negative fractions?
    Posted in the Algebra Forum
    Replies: 13
    Last Post: September 24th 2006, 05:36 PM

Search Tags


/mathhelpforum @mathhelpforum