Estimate the magnitude of the error in approximating $\sin (1)$ using a third degree Taylor polynomial about x = 0.
A)0.0125
B)0.0333
C)0.0417
D)0.0625

Question

Quizplus · Accepted Answer

The error in approximating $\sin(x)$ using a third degree Taylor polynomial is given by the next term in the Taylor series, which is $\frac{x^5}{5!}$. For $x = 1$, this is $\frac{1^5}{120} = 0.00833$. However, since the Taylor polynomial is centered at 0, the error is bounded by the maximum value of the next derivative term over the interval [0,1], which is $\frac{1}{5!} = 0.0417$.

Estimate the Magnitude of the Error in Approximating sin⁡(1)\sin (1)sin(1) Using a Third Degree Taylor Polynomial About X = 0

Estimate the Magnitude of the Error in Approximating $\sin (1)$ Using a Third Degree Taylor Polynomial About X = 0