Taylor Series of degree 3 centered at 0 for cos(x)

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RohDog

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I had to calculate the Taylor polynomial of degree 3 centered at 0 for cos(x). This was 1- .5x^2

I now have to calculate the maximum error for the approximation at 6pi/7 and 9pi/7. How do I do this?

I also have to calculate the error for the approximation at 0, pi/2, and pi. How do I do this?

Thanks
 
Re: Taylor Series

Calculate the exact values. Use your calculator or your head, if it is a value you should know.
 
Do I compare the value I get by plugging it into the calculator to the one I get by plugging it into the Taylor polynomial?
 
since the series for cos(x) is alternating, the error will be less than the first omitted term.
 
Ok, I've figured out everything except how to calculate the maximum error for the approximation at 6pi/7 and 9pi/7? Can you expand on this? I don't know where to begin.
 
RohDog said:
Ok, I've figured out everything except how to calculate the maximum error for the approximation at 6pi/7 and 9pi/7? Can you expand on this? I don't know where to begin.
Click to expand...

read my last post.
 
It is a cosine function, so an upper bound on the error couldn't be much greater than that, but that hardly is useful.

Did you read the post? You do not need the first term. You need the "first omitted term". You must read carefully.

If you continued the series until you added another term, the x^4 term, then that term, evaluated where desired, would be a more rational upper bound on the error.
 
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