Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By veileen

Math Help - Solving the limit!! LIMIT x -> 0+ sqrt(x) * e^(sin(pi/x))

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    Arizona
    Posts
    4

    Angry Solving the limit!! LIMIT x -> 0+ sqrt(x) * e^(sin(pi/x))

    Help with SOLVING!!! {LIMIT x -> 0+} sqrt(x) * e^(sin(pi/x))

    I know the Limit is zero I want to know how. Here's what I got:



    {LIMIT x -> 0+} sqrt(x) * e^(sin(pi/x)) (I assume continuity so i plug n chug)

    {LIMIT x -> 0+} sqrt(0) * e^(sin(pi/0)) => {LIMIT x -> 0+} 0 * e^(sin(pi/x)) = INDETERMINATE

    {LIMIT x -> 0+} sqrt(x) * e^((pi/x)*(sin(pi/x))/pi/x)) ({LIMIT x -> 0+} {LIMIT x -> pi/x+} (sin(pi/x))/pi/x) = 1)

    {LIMIT x -> 0+} sqrt(x) * e^(pi/x) (I'm stuck here i plug in 0 for x and i get e^ (pi/0))
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Mar 2011
    From
    Awetuouncsygg
    Posts
    182
    Thanks
    12

    Re: Solving the limit!! LIMIT x -> 0+ sqrt(x) * e^(sin(pi/x))

    \lim_{x\rightarrow0+}\frac{\sin \frac{\pi}{x}}{\frac{\pi}{x}} is not necessarily 1, because \frac{\pi}{x}\xrightarrow[]{x\rightarrow 0+}\infty.

    The remarkable limit is \lim_{x\rightarrow 0}\frac{\sin x}{x}=1.


    Edit:

    -1\leq \sin \frac{\pi}{x}\leq 1 \Rightarrow e^{-1} \leq e^ {\sin \frac{\pi}{x}} \leq e

    \Rightarrow e^{-1}\sqrt x  \leq e^ {\sin \frac{\pi}{x}}\sqrt x  \leq e\sqrt x


    \lim_{x\rightarrow 0+} e^{-1}\sqrt x=0
    \lim_{x\rightarrow 0+} e\sqrt x=0

    So the limit is 0.
    Last edited by veileen; February 17th 2013 at 12:59 PM.
    Thanks from kram19
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2012
    From
    Arizona
    Posts
    4

    Re: Solving the limit!! LIMIT x -> 0+ sqrt(x) * e^(sin(pi/x))

    Thank you for the reasonable answer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. limit 1/sqrt(n)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 14th 2013, 10:33 AM
  2. limit of (sqrt(3x+6)-3)/(x-1) | x->1
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 9th 2010, 11:06 AM
  3. Replies: 2
    Last Post: April 21st 2010, 07:27 PM
  4. Limit of sqrt(2*sqrt(2)) sequence
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 4th 2010, 04:06 AM
  5. sqrt limit question..
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 13th 2009, 10:43 AM

Search Tags


/mathhelpforum @mathhelpforum