Exercise 7.4 : Series Expansions: Maclaurin’s and Taylor’s Series

EXERCISE 7.4

1. Write the Maclaurin series expansion of the following functions:

(i) ex

(ii) sin x

(iii) cos x

(iv) log(1- x) ; –1 ≤ x < 1

(v) tan-1 (x) ; –1 ≤ x â‰¤ 1

(vi) cos2 x

2. Write down the Taylor series expansion, of the function log x about x = 1 upto three non-zero terms for x > 0.

3. Expand sin x in ascending powers x â€“ Ï€/4 upto three non-zero terms.

4. Expand the polynomial f (x) = x2 â€“ 3x + 2 in powers of x â€“ 1.

Answers:

(4) f (x) = − ( x âˆ’1) + ( x âˆ’1)2