Taylor Polynomials and Numerical Analysis

[mynorka]

Homework Statement

Use a Taylor Polynomial about pi/4 to approximate cos(42){degrees} to an accuracy of 10^-6.

*To get an accuracy of 10^-6, use the error term to determine an nth Taylor Polynomial to use.

Homework Equations

x = 45 or pi/4, x0 = 42 or 7pi/30

cos(x) = Pn(x) + Rn(x)

Polynomial Term - Pn(x) = ∑f^(k)(x-x0)^k/(k)!

Error Term - Rn(x) = f^(n+1)(ζ(x))(x-x0)^(n+1)/(n+1)!

The Attempt at a Solution

(pi/60)^n/(n+1)! < ((-60/pi)*10^-6)/pi

^I get stuck at this part. I'm supposed to solve for n, but the left-hand side of this inequality confuses me.

 

[Ray Vickson]

Homework Statement

Use a Taylor Polynomial about pi/4 to approximate cos(42){degrees} to an accuracy of 10^-6.

*To get an accuracy of 10^-6, use the error term to determine an nth Taylor Polynomial to use.

Homework Equations

x = 45 or pi/4, x0 = 42 or 7pi/30

cos(x) = Pn(x) + Rn(x)

Polynomial Term - Pn(x) = ∑f^(k)(x-x0)^k/(k)!

Error Term - Rn(x) = f^(n+1)(ζ(x))(x-x0)^(n+1)/(n+1)!

The Attempt at a Solution

(pi/60)^n/(n+1)! < ((-60/pi)*10^-6)/pi

^I get stuck at this part. I'm supposed to solve for n, but the left-hand side of this inequality confuses me.

What are you doing? We have $|\text{error}| \leq (\pi/60)^{n+1}/(n+1)!$, and this must not exceed $10^{-6}$.

 

[member 428835]

this is pretty tough to read. perhaps put it in latex and then we can check it out