FP2 - Unit 3

Question 1

What is the Maclaurin series used for?

Answer 1

To show functions f and g agree to the nth degree at x=0, f^(r)(0) = g^(r)(0)

Question 2

Maclaurin expansion for e^x

Answer 2

1 + x/1! + x²/2! + x³/3! + ….. + x^r/r!

Question 3

Maclaurin expansion for sinx

Answer 3

x - x³/3! + x^5/5!+…+(-1)x^2r+1 / (2r+1)!

Question 4

Maclaurin expansion for cosx

Answer 4

1 - x²/2! + x^4/4! - x^6/6! ….+(-1)^r-1 x^r/r

Question 5

Maclaurin expansion for ln(1+x)

Answer 5

x - x^2/2 + x^3/3 - x^4/4