The alternating sign of the terms is VERY helpful.
What is the size of the first term omitted on the desired interval?
Completely lost, all help appreciated
1) Bound the error in the approximation
sin(x) ≈ x
for -pi/4 ≤ x ≤ pi/4
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Let p(x) be the Taylor polynomial of degree n of the function
f(x) = log(1-x) about a = 0.
How large should n be to have
| f(x)-p(x) | ≤ 10^(-4) for -1/2 ≤ x ≤ 1/2 ?
For -1 ≤ x ≤ 1/2
The error is less than the first term not used in the approximation
|-x^3/3!| < pi^3/(4^3*3)= pi^3/384.
So is that the answer??
If they ask, "What is the taylor polynomial of degree 3?"
Do you make sure that you have x^3 and no higher degree? Or do you keep 3 terms or? How do you know what's degree 3, etc. Thanks.
That's the idea, but are you sure that's where the maximum value occurs, AT ? Also, 3! = 6, not 3. 3! = 3*2*1
Quit when you have a term in x^3 or of higher degree. For example, I dare you to find a degree 3 polynomial for f(x) = cos(x). Please don't count the number of terms while looking for degree.If they ask, "What is the taylor polynomial of degree 3?"