Ellie C.

asked • 03/03/23

Taylor series question: finding a value that verifies ...

I am struggling with the attached question. I would really appreciate an explanation -- thank you!


The Taylor polynomial P sub n equals the summation from n equals 1 to infinity of quantity negative 1 end quantity to the n power times x to the n power over n factorial about x = 0 is used to approximate the value of the function f at x equals one fourth period Find the value that verifies the absolute value of quantity P sub 3 of one fourth minus f of one fourth end quantity is less than 1 over 5000 period

Choices:

 P sub 3 of one fourth equals negative 1 over 384 P sub 3 of one fourth equals 1 over 384 P sub 4 of one fourth equals negative 1 over 6144 P sub 4 of one fourth equals 1 over 6144


1 Expert Answer

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Yefim S. answered • 03/03/23

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If(1/4)- P3(1/4)I < 1/5000;

So, -1/5000 + P3(1/4) < f(1/4) < 1/5000 + P3(1/4);

P3(1/4) = - 85/384

-1/5000 - 85/384 < f(1/4) < 1/5000 - 85/384;

-0.2216 < f(1/4) < - 0.2212

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Ellie C.

Thank you! I understand that part, but how would I find one of the answer choices from there? Thank you so much for your help once again.
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03/03/23

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