Question

The Taylor series expansion of 3 sin x + 2 cos x is

(A) 2 + 3x - x2 - x3/2 + .....

(B) 2 - 3x + x2 - x3/2

(C) 2 + 3x + x2 + x3/2 + .....

(D) 2 - 3x - x2 + x3/2 + .....

Answer 1

Correct option (A) 2 + 3x - x2 - x3/2 + .....

Explanation:

3sinx + 2cosx = 3(x - x3/3! + ....) + 2(1 - x2/2! + ...)

= 2 + 3x - x2 - x3/2 + .....