Question

How do you find the Maclaurin Series for `e^(sinx)`?

Answer 1

`e^sinx = e^(sin(0))+ x cos(0) e^(sin(0)) + 1/2 x^2(cos^2 (0) - cos(0) sin(0))e ^(sin(0)) +....=1 + x+ x^2/2 +.....`

Explanation:

Using f(x) = f(0) + xf'(0) + x^2/2 f''(0) + higher order terms which can be computed in a similar manner.