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Answer to Question #1193 in Calculus for Mert Evren

Question #1193
What is the first three non-zero terms of the Taylor series for the function f(x)=cos(x) about x=0?
Expert's answer
The first terms of Taylor series for the function f(a) are
f(a) + f'(a) (x-a)/1! + f''(a)(x-a)2 / 2! + ...
Let's find it for f(x) = cos(x) and a = 0:
cos(0) + (-sin(0))(x-0)/1! + (-cos(0))x2 / 2! + sin(0) x3/3! + cos(0) x4 / 4! = 1 + 0 - x2/2 + 0 + x4/24
= 1 - x2/2 +x4/24

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Assignment Expert
14.12.10, 13:18

You & are welcome.

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