Question

Write the cubic term for the Taylor series expansion of f(x) = sin(x) at c = pi/4

I did the work, can you please check for me whether my work is right?

Answer 1

Explanation:

Close, the second term should have an exponent of 1.

f(x) = f(c) + f'(c) (x−c)¹/1! + f''(c) (x−c)²/2! + f'''(c) (x−c)/3!

f(x) = 1/√2 + 1/√2 (x−π/4) − 1/(2√2) (x−π/4)² − 1/(6√2) (x−π/4)³