Which of the following functions equals the power series ?

Question

Which of the following functions equals the power series  ?

	sin(x)
	cos(x)
	ln(x)
	ex

Answer 1

Try derivatives for Maclaurin series for each that match the coefficients

sin:

f(0) = sin(0) = 0

f'(0) = cos(0) = 1 No

cos:

f(0) = cos(0) = 1

f'(0) = -sin(0) = 0

f"(0) = -cos(0) = -1

f'''(0) = sin(0) = 0

f^iv(0) = cos(0) = 1 A candidate

ln:

f(0) = ln(0) undefined. so NO .... Usually ln(x+1) is converted to Maclaurin series

e^x:

f(0) = e⁰ = 1

f'(0) = e⁰ = 1 NO

The answer is B, cos(x)