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

  • #1
41
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.
 

Answers and Replies

  • #3
34,004
5,658
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.
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
$$\frac{1}{\lim_{w \to w_0} \frac{e^w - e^{w_0}}{w - w_0}} $$
 
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Likes thegirl
  • #4
41
1
Omg thank you so much!!!!!!!!!!!
 
  • #5
mathman
Science Advisor
7,858
446
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
$$\frac{1}{\lim_{w \to w_0} \frac{e^w - e^{w_0}}{w - w_0}} $$
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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Likes thegirl

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