In the Taylor series expansion of e^x + sin x about the point x = π, the coefficient
- A. e^π
- B. 0.5 e^π
- C. e^(π+1)
- D. e^(π-1)
Answer: B. 0.5 e^π
Explanation: The Taylor series coefficient for (x − π)² is f''(π)/2!. f'(x) = e^x + cos x, f''(x) = e^x − sin x. At x = π, f''(π) = e^π − sin π = e^π. Thus, coefficient = e^π/2! = 0.5 e^π.