Results 1 to 5 of 5

Math Help - limits help

  1. #1
    Newbie
    Joined
    Sep 2011
    Posts
    11

    limits help

    Find the limit by interpreting the expression as an appropriate derivative.
    lim [(10^h)-1]/h
    h-->0

    I've been staring at this problem forever and don;t know where to begin, please help!
    Last edited by mr fantastic; September 10th 2011 at 02:35 PM. Reason: Title.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,560
    Thanks
    1425

    Re: limits help please!

    Quote Originally Posted by calculuskangaroo View Post
    Find the limit by interpreting the expression as an appropriate derivative.
    lim [(10^h)-1]/h
    h-->0

    I've been staring at this problem forever and don;t know where to begin, please help!
    Are you allowed to use L'Hospital's Rule?

    \displaystyle \begin{align*} \lim_{h \to 0}\frac{10^h - 1}{h} &= \lim_{h \to 0}\frac{\frac{d}{dh}\left(10^h - 1\right)}{\frac{d}{dh}\left(h\right)} \\ &= \lim_{h \to 0}\frac{10^h\ln{(10)}}{1} \\ &= \ln{(10)}\lim_{h \to 0}10^h \\ &= \ln{(10)}\cdot 10^0 \\ &= \ln{(10)} \cdot 1 \\ &= \ln{(10)} \end{align*}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2011
    Posts
    11

    Re: limits help please!

    thank you so much! can you just explain how you got from d/dh(10^h-1) to 10^h(ln10)
    thank you!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,560
    Thanks
    1425

    Re: limits help please!

    Quote Originally Posted by calculuskangaroo View Post
    thank you so much! can you just explain how you got from d/dh(10^h-1) to 10^h(ln10)
    thank you!
    \displaystyle \frac{d}{dx}\left(a^x\right) = a^x\ln{(a)}, and the derivative of a constant is 0.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2011
    Posts
    11

    Re: limits help please!

    ohhh okay! i got it now thank you so much
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. limits
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 22nd 2009, 11:06 PM
  2. Using limits to find other limits
    Posted in the Calculus Forum
    Replies: 7
    Last Post: September 18th 2009, 05:34 PM
  3. Function limits and sequence limits
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: April 26th 2009, 01:45 PM
  4. Limits Help
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 11th 2008, 06:39 PM
  5. [SOLVED] [SOLVED] Limits. LIMITS!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 25th 2008, 10:41 PM

Search Tags


/mathhelpforum @mathhelpforum