Electronics and Communication Engineering - Exam Questions Papers - Discussion

28. 

In the Taylor series expansion of exp(x) + sin(x) about the point x = p, the coefficient of (x - p)2 is

[A]. exp (p)
[B]. 0.5 exp (p)
[C]. exp (p) + 1
[D]. exp (p) - 1

Answer: Option B

Explanation:

f(x) = ex + sin x

Coefficient of (x - p)2 = 1 / 2! f''(x)

f'(x) = ex + cos x

f'(x) = ex - sin x

f''(x)|x=p = ep

Thus coefficient of (x - p)2 = 0.5 .


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