1. Taylor Polynomials redux

I need to know this for a quiz tomorrow!

1. Let f(x)=log(x) and determine Subscript[p, 2](x) where a=1, b=2. As above, determine the bound for the maximum error and make a graph.

2.Do the same for f(x)=(1-x)/(1+x) on [.5 , 1] (i.e., a=.5, b=1).

Thanks

2. Originally Posted by swimmerxc
1. Let f(x)=log(x) and determine Subscript[p, 2](x) where a=1
I do the first one. So you are finding a Taylor polynomial centered at $1$ for $\log x$ which is equivalent for a Taylor polynomial centered at $0$ for $f(x) = \log (x+1)$.
The Taylor polynomial of degree $2$ is: $x - \frac{x^2}{2}$. If $a>-1$ then $f'$ is bounded on $(a,\infty)$ by $1/(a+1)$. Thus, $\left| R_3(x) \right| \leq \frac{1}{3!(a+1)}$

3. Thanks but I don't get what you did with b=2?

4. Originally Posted by swimmerxc
Thanks but I don't get what you did with b=2?
I understood that a=1 means a Taylor polynomial centered at 1. And b=2 to be a Taylr polynomial centered at 2. Thus, it was two seperate problems, and I did the first part with a=2. Is that what you meant? If

5. no, I dont get the way how you solve the problem, can you please show me the steps? we were taught to use the Mean Value Theorem

Thanks