Calculus

Taylor Series

Taylor Series - Error Bounds

         

Find the error bound for the 4th4^\text{th} degree polynomial of

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

Find the error bound for the 4th4^\text{th} degree polynomial of

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

What is the maximum possible error of the 10th10^\text{th} degree polynomial of

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

What is the maximum possible error of the 1st1^\text{st} degree polynomial of

f(x)=1+x  centered at  x=0  on the interval  [0.01,0.01]?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 2nd2^\text{nd} degree polynomial of

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

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