Results 1 to 3 of 3

Math Help - Limit of e

  1. #1
    Newbie
    Joined
    Jan 2006
    Posts
    20

    Limit of e

    Let f be the function given by f(x)=2xe^(2x)

    a) Find Lim as x reaches infinity and negative infinity (i.e. Lim )
    x->infinity/-infinity

    b) What is the range of f?

    Thanks a lot for the help, e always confuses me and i have no idea how i should do this problem.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by aussiekid90 View Post
    Let f be the function given by f(x)=2xe^(2x)

    a) Find Lim as x reaches infinity and negative infinity (i.e. Lim )
    x->infinity/-infinity
    As both x and e^{2x} go to infinity as x goes to + \infty clearly the

    \lim_{x \to \infty} 2x e^{2x}=\infty.

    Now as x \to -\infty,\ x \to -\infty and e^{2x} \to 0, so we gave an indeterminent form, so we apply L'Hopitals rule

    Put:

    <br />
f(x)=\frac{2x}{e^{-2x}}<br />

    then:

    <br />
\lim_{x \to -\infty} f(x) = \lim_{x \to -\infty} \frac{2(-2)}{e^{-2x}}=0<br />

    b) What is the range of f?

    Thanks a lot for the help, e always confuses me and i have no idea how i should do this problem.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by aussiekid90 View Post
    b) What is the range of f?

    Thanks a lot for the help, e always confuses me and i have no idea how i should do this problem.
    We know that f(x) goes to +\infty as x becomes large , and goes to 0
    as x goes to -\infty. Also differentiating and setting the derivative to zero
    shows that f(x) has a minimum of -e^{-1} at x=-1/2.

    So the range of f is [-e^{-1}, +\infty).

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 12
    Last Post: August 26th 2010, 11:59 AM
  2. Replies: 1
    Last Post: August 8th 2010, 12:29 PM
  3. Replies: 1
    Last Post: February 5th 2010, 04:33 AM
  4. Replies: 16
    Last Post: November 15th 2009, 05:18 PM
  5. Limit, Limit Superior, and Limit Inferior of a function
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 3rd 2009, 06:05 PM

Search Tags


/mathhelpforum @mathhelpforum