Calculus
# Taylor Series

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

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