Loading....
Coupon Accepted Successfully!

 

Definition (the number e)

The limiting value of 87137.png when n tends to infinity is denoted by e.
 
i.e., 87143.png + … ∞
= 2.71 (nearly)

Expansion of exponential series

For x R, ex = 1 + 87261.png
 
or ex = 87271.png.
 
Tn + 1 = General term in the expansion of ex = xn/(n!) and coefficient of xn in ex = 1/n!

Exponential function ax, where a > 0

ax 87277.png
87283.png

Some standard results from exponential series

  1. 87292.png + … ∞ = e – 1
  2. 87298.png + … ∞ = e – 2
  3. 87322.png
  4. 87332.png
  5. 87338.png
∴ Tn + 1 = General term in the expansion of xax
= 87344.png and coefficient of xn in eax = 87353.png




Test Your Skills Now!
Take a Quiz now
Reviewer Name