Power Series and Limits

Question 1

What is the Taylor series?

Answer 1

f(x) = f(xo) + f’(xo)(x-xo) + … + f^n(xo)/n! (x - xo)^n

Question 2

What is the Taylor expansion for e^x?

Answer 2

e^x = 1 + x + x^2/2! + … + x^n/n!

Question 3

What is the Taylor expansion for sinx?

Answer 3

sinx = x - x^3/3! + … + (-1)^n.x^(2n + 1)/(2n + 1)!

Question 4

What is the Taylor expansion for cosx?

Answer 4

cosx = 1 - x^2/2! + … + (-1)^n.x^(2x)/(2n)!