Question

Use the Error Bound for Taylor Polynomials to give a good bound

for the error for the nth degree Taylor polynomial
about x=0 approximating sin(x) on the
interval [0,0.9]
error bound =

Answer 1

To find the error bound for the nth degree Taylor polynomial approximating sin(x) on the interval [0,0.9], use the Error Bound for Taylor Polynomials formula by determining the maximum value of the (n+1)th derivative of sin(x) and substituting it into the formula.

Step-by-step explanation:

To find a good bound for the error of the nth degree Taylor polynomial approximating sin(x) on the interval [0,0.9], we can use the Error Bound for Taylor Polynomials formula. The formula is given by:

Error Bound = ((M * x^(n+1))/(n+1)!), where M is the maximum value of the (n+1)th derivative of sin(x) on the interval [0,0.9].

To determine M, we can find the (n+1)th derivative of sin(x), evaluate it at x=0.9, and take the absolute value to find the maximum value. Finally, we can substitute the values of M and n into the formula to calculate the error bound.