Asked by Anonymous
Please help. I got stuck on this problem all week. And please show steps. Use Taylor Inequality to estimate approximation f(x)Tn(x) when x lies in the given interval. Round your answer to six decimal places. a=3, n=3, 2.5<=x<=3.5?
Answers
Answered by
oobleck
well, the formula is
|R<sub><sub>k</sub></sub>(x)| <= M/(n+1)! |x-a|<sup><sup>n+1</sup></sup>
Now, 2.5 <= x <= 3.5 means |x-3| <= 1/2
Using your values, that means that
|R<sub><sub>3</sub></sub>(x)| <= M/4! * 1/16
where M is a bound on the 4th derivative of f(x), which you have not specified, but maybe you can fix that
|R<sub><sub>k</sub></sub>(x)| <= M/(n+1)! |x-a|<sup><sup>n+1</sup></sup>
Now, 2.5 <= x <= 3.5 means |x-3| <= 1/2
Using your values, that means that
|R<sub><sub>3</sub></sub>(x)| <= M/4! * 1/16
where M is a bound on the 4th derivative of f(x), which you have not specified, but maybe you can fix that
Answered by
Anonymous
The function is f(x)=ln(1+2x) but the 4th derivative I don't know. So, how do I plug in now?
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.