1. ## Maclauren polynomials

A couple of problems:

1. Find the Maclauren Polynomial of degree 4 for the function f(x) = x/(x+1)

2. Determine the degree of the Maclauren polynomial required for the error in the approximation of the function, f(x) = cos(x) to be less than 0.001, if x=0.1

Thanks!

2. Originally Posted by bakanagaijin
A couple of problems:

1. Find the Maclauren Polynomial of degree 4 for the function f(x) = x/(x+1)
Do you know the definition of a Maclaurin series? If yes show us what you have done.

2. Determine the degree of the Maclauren polynomial required for the error in the approximation of the function, f(x) = cos(x) to be less than 0.001, if x=0.1
Because the series for cos has alternating signs the error for x=0.001 is less than the first neglected term. Alternativley use one of the remainder formulas for Taylor series.

RonL

3. Originally Posted by bakanagaijin
A couple of problems:

1. Find the Maclauren Polynomial of degree 4 for the function f(x) = x/(x+1)

2. Determine the degree of the Maclauren polynomial required for the error in the approximation of the function, f(x) = cos(x) to be less than 0.001, if x=0.1

Thanks!
utilizing the fact that only for $\displaystyle x\in(-1,1)$ $\displaystyle \frac{1}{1+x}=\sum_{n=0}^{\infty}(-1)^{n}x^{n}$ you can easily extrapolate the first answer by taking the product of that series and x...then expand until the desired order of polynomial is acheived