Results 1 to 4 of 4

Math Help - Verify limit?

  1. #1
    Newbie
    Joined
    Sep 2012
    From
    United States
    Posts
    6

    Verify limit?

    Hi All,

    I've been wrapping my head around this limit problem and I think my error is stemming from some bad factoring but I could be wrong:

    Limit as x approaches 0 from positive infinity
    ((3^x)-(3^-x))/((3^x)+(3^-x)

    The answer should be: approaches 1.

    The answer I always get is 0.

    Any help would be much appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,662
    Thanks
    1488

    Re: Verify limit?

    Quote Originally Posted by jokem View Post
    Hi All,

    I've been wrapping my head around this limit problem and I think my error is stemming from some bad factoring but I could be wrong:

    Limit as x approaches 0 from positive infinity
    ((3^x)-(3^-x))/((3^x)+(3^-x)

    The answer should be: approaches 1.

    The answer I always get is 0.

    Any help would be much appreciated!
    \displaystyle \begin{align*} \frac{3^x - 3^{-x}}{3^x + 3^{-x}} &= \frac{3^x\left( 3^x - 3^{-x}\right)}{3^x \left( 3^x + 3^{-x} \right)} \\ &= \frac{3^{2x} - 1}{3^{2x} + 1} \\ &= 1 - \frac{2}{3^{2x} + 1} \end{align*}

    I agree that this should approach 0 as you make x approach 0.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2012
    From
    Planet Earth
    Posts
    196
    Thanks
    49

    Re: Verify limit?

    You don't even need to take limits. This function is continuous on all of \mathbb{R}.

    f(0) does equal 0.

    But the limit at infinity is 1... maybe the problem was read or interpreted wrong?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2012
    From
    United States
    Posts
    6

    Re: Verify limit?

    Wow, thank you very much!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Verify the limit
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: April 26th 2011, 02:07 PM
  2. Please verify
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 25th 2010, 06:55 PM
  3. Please verify
    Posted in the Algebra Forum
    Replies: 3
    Last Post: January 14th 2010, 10:46 PM
  4. verify?!
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 2nd 2008, 08:06 AM
  5. verify???
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 5th 2008, 04:25 PM

Search Tags


/mathhelpforum @mathhelpforum