Which of the following functions equals the power series 1 minus x squared over 2 factorial plus x to the 4th power over 4 factorial, etc ?

Question

Which of the following functions equals the power series  ?

A	sin(x)
B	cos(x)
C	ln(x)
D	ex

Answer 1

Looks like the Maclaurin series for cos(x), Answer B

You can verify this

f(0) = cos(0) = 1

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

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

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

:

f(x) = (1)x⁰/0! + (-1)(0)x¹/1! + (-1)x²/2! + (0)x³/3! + 1x⁴/4! + ....

= 1-x²/2!+ x⁴/4! + ....