# math taylor polynomial help?

Write the Taylor polynomial T5(x) for the function f(x)=sin(x) centered at x=0.

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- 8 years agoFavorite Answer
sin(x) taylor polynomial = x - x^3/3! + x^5/5!

Taylor polynomial: f(a) + (x-a)f '(a) + (x-a)^2f "(a)/2! + (x-a)^3f "'(a)/3! + (x-a)^4f ⁴(a)/4! + (x-a)^5f⁵(a)/5!

a = 0

f(x) = sin(x)

f '(x) = cos(x)

f "(x) = -sin(x)

f "'(x) = -cos(x)

sin(0) + (x-0)cos(0) - (x-0)^2sin(0)/2! - (x-0)^3cos(0)/3! + (x-0)^4sin(0) +(x-0)^5cos(0)/5!

= 0 + x - 0 - x^3/3! + 0 + x^5/5! = x - x^3/3! + x^5/5!

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