# Taylor Polynomial Error

Discussion in 'Math' started by meichberg92, May 12, 2014.

1. ### meichberg92 Thread Starter New Member

May 12, 2014
2
0
Hey I need help with this problem guys!

How do I find, using Taylor's Theorem, the error of the taylor polynomial of f(x)=sqrt(x) of degree 2 to approximate sqrt(8)?

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

Feb 24, 2006
11,121
2,170
3. ### meichberg92 Thread Starter New Member

May 12, 2014
2
0
What about the second question? I dont think that has to do with it.

Nov 9, 2007
5,005
519
5. ### Papabravo Expert

Feb 24, 2006
11,121
2,170
I think that sin(x) and the polynomial you gave are equivalent for the first three terms. Since this is an alternating series, a bound should be the absolute value of the next term.

Last edited: May 13, 2014
6. ### studiot AAC Fanatic!

Nov 9, 2007
5,005
519
Well spotted papabravo!

Of course there are only three terms stated in the second part.

7. ### Papabravo Expert

Feb 24, 2006
11,121
2,170
There might possibly be better bounds. For example a Chebyshev approximation has a much better absolute error bound for a given number of terms over the entire interval of approximation, which is typically [-1,1]