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# Taylor Series

The Taylor series is a polynomial of infinite degree used to represent functions like sine, cube roots, and the exponential function. They're how some calculators (and Physicists) make approximations.

# Taylor Series - Error Bounds

Find the error bound for the $$4^\text{th}$$ degree polynomial of

$f(x)=\sin x ~\text{ centered at }~ x=0 ~\text{ on the interval }~ [0,2\pi].$

Find the error bound for the $$4^\text{th}$$ degree polynomial of

$f(x)=\cos x ~\text{ centered at }~ x=0 ~\text{ on the interval }~ [0,2\pi].$

What is the maximum possible error of the $$10^\text{th}$$ degree polynomial of

$f(x)=e^{x} ~\text{ centered at }~ x=0 ~\text{ on the interval }~ [-2,2]?$

What is the maximum possible error of the $$1^\text{st}$$ degree polynomial of

$f(x)=\sqrt{1+x} ~\text{ centered at }~ x=0 ~\text{ on the interval }~ [-0.01,0.01]?$

What is the maximum possible error of the $$2^\text{nd}$$ degree polynomial of

$f(x)=\ln(1+x) ~\text{ centered at }~ x=0 ~\text{ on the interval }~ [-0.1,0.1]?$

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