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Finding the limit of lim w-->wo ((exp(w)-exp(wo))/(w-wo))^-1

  1. Oct 27, 2015 #1
    Hi,

    I know that when you take this limit it is equal to e^-wo, but I was just wondering how you got there when taking the limit?

    lim w-->wo ((exp(w)-exp(wo))/(w-wo))^-1 = 1/e^wo

    w and wo are both two points within the same plane.
     
  2. jcsd
  3. Oct 27, 2015 #2
    Theres a better layout of the equation with x and y instead of w and wo
     

    Attached Files:

  4. Oct 27, 2015 #3

    Mark44

    Staff: Mentor

    You can evaluate the expression inside the outer parenthese using L'Hopital's Rule.

    $$\lim_{w \to w_0} \left(\frac{e^w - e^{w_0}}{w - w_0} \right)^{-1}$$
    The above is equal to
    $$\frac{1}{\lim_{w \to w_0} \frac{e^w - e^{w_0}}{w - w_0}} $$
     
  5. Oct 27, 2015 #4
    Omg thank you so much!!!!!!!!!!!
     
  6. Oct 27, 2015 #5

    mathman

    User Avatar
    Science Advisor
    Gold Member

    The denominator in the last expression is simply [itex]\frac{d}{dw}e^w[/itex] evaluated at [itex]w=w_0[/itex].
     
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