Finding Error on Taylor Polynomials using Taylor's Theorem

[meichberg92]

(a) Use Taylor's Theorem to estimate the error in using the Taylor Polynomial of f(x)=sqrt{x} of degree 2 to approximate sqrt{8}. (The answer should be something like 1/2 * 8^{-7/2}.

(b) Find a bound on the difference of sin(x) and x- x^{3}/6 + x^{5}/120 for x in [0,1]This is a problem on a problem sheet that isn't for homework but there are NO solutions. Any help toward a solution would be appreciated.

 

[Ray Vickson]

(a) Use Taylor's Theorem to estimate the error in using the Taylor Polynomial of f(x)=sqrt{x} of degree 2 to approximate sqrt{8}. (The answer should be something like 1/2 * 8^{-7/2}.

(b) Find a bound on the difference of sin(x) and x- x^{3}/6 + x^{5}/120 for x in [0,1]


This is a problem on a problem sheet that isn't for homework but there are NO solutions. Any help toward a solution would be appreciated.

Use the formula for the error in a Taylor series after the nth term. It is widely available; just Google 'Taylors Theorem'.