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))x^{2} / 2! + sin(0) x^{3}/3! + cos(0) x^{4} / 4! = 1 + 0 - x^{2}/2 + 0 + x^{4}/24

= 1 - x^{2}/2 +x^{4}/24

f(a) + f'(a) (x-a)/1! + f''(a)(x-a)

Let's find it for f(x) = cos(x) and a = 0:

cos(0) + (-sin(0))(x-0)/1! + (-cos(0))x

= 1 - x

## Comments

Assignment Expert14.12.10, 13:18You & are welcome.

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