The question asks for the coefficient of
(x - π)2
in the Taylor series expansion of
exp(x) + sin(x)
about the point x = π.
To find this coefficient, we need to calculate the second derivative of
exp(x) + sin(x), evaluate it at
x = π, and then divide by 2!.
The second derivative of
exp(x) + sin(x) is:
exp(x) - sin(x), and its value at
x = π
is:
exp(π) - sin(π) = exp(π).
Therefore, the coefficient of
(x - π)2
in the Taylor series expansion of
exp(x) + sin(x)
about the point
x = π
is: exp(π)/2! = eπ/2.
Therefore, the answer is:
0.5eπ