1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Exponential question

  1. Oct 15, 2011 #1
    How do you differentiate lim (2^h - 1)/h ?
    h --> 0
    I would like to know how to do it algebraically instead of picking values of x that approach 0 and plugging it in to 2^x.
     
  2. jcsd
  3. Oct 15, 2011 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I presume you mean how do you evaluate that limit. If you know the derivative of ex you can do it this way:

    [tex]\lim_{h\rightarrow 0}\frac{2^h-1}{h}=
    \lim_{h\rightarrow 0}\frac{e^{h\ln 2}-1}{h}=
    (\ln 2)\ \lim_{h\rightarrow 0}\frac{e^{h\ln 2}-1}{h\ln 2}[/tex]

    Not let t = h ln(2) giving

    [tex](\ln 2)\ \lim_{t\rightarrow 0}\frac{e^{t}-1}{t}[/tex]

    That gives ln(2) as the answer because the limit of the fraction is 1. You can see that either by recognizing that difference quotient as the derivative of ex at x = 0 or by applying L'Hospital's rule to it if you have had that.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Exponential question
Loading...