Results 1 to 4 of 4

Math Help - sinx/x as x goes to infinity

  1. #1
    Member
    Joined
    Feb 2008
    Posts
    184

    sinx/x as x goes to infinity

    I know Limit goes to 1 as x tends to zero but what happens when x tends to infinity. \lim_{x \rightarrow infinity} \frac{\sin x}{x}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by charikaar View Post
    I know Limit goes to 1 as x tends to zero but what happens when x tends to infinity. \lim_{x \rightarrow infinity} \frac{\sin x}{x}

    lemma: if f(x) is bounded in some neighborhood of x_o and g(x) \xrightarrow [x\to x_0] {} 0, then
    f(x)g(x) \xrightarrow [x\to x_0] {} 0
    If the limit is when x \rightarrow \infty then f(x) must be bounded for x>R\in \mathbb{R}, for some real number R

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,707
    Thanks
    627
    Hello, charikaar!

    I know: . \lim_{x\to0}\frac{\sin x}{x} \:=\:1

    but what happens when x tends to infinity? . \lim_{x \to \infty} \frac{\sin x}{x}

    The numerator oscillates between -1 and +1,
    . . while the denominator tends to infinity.

    Therefore: . \lim_{x\to\infty}\frac{\sin x}{x} \;=\;0

    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Bruno J.'s Avatar
    Joined
    Jun 2009
    From
    Canada
    Posts
    1,266
    Thanks
    1
    Awards
    1
    Well 0\leq |\sin x| \leq 1, so for x > 0,

    0 \leq \frac{|\sin x|}{x} \leq \frac{1}{x}

    By the squeeze theorem, \frac{\sin x}{x}\rightarrow 0 as x \rightarrow \infty.

    Edit : damn, beat me to it.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. ((1+sinx+icosx)/(1+sinx-icos))^n
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: November 28th 2011, 07:06 PM
  2. Replies: 6
    Last Post: April 23rd 2011, 12:05 PM
  3. Replies: 1
    Last Post: March 25th 2011, 12:27 AM
  4. Integral of Ln(Sinx)/Sinx
    Posted in the Calculus Forum
    Replies: 7
    Last Post: January 11th 2010, 02:18 AM
  5. find y' if y=(sinx)^2 + 2^(sinx)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 23rd 2009, 05:00 PM

Search Tags


/mathhelpforum @mathhelpforum