1. Determine Taylor's remainder formula (Property 2.9) for the Taylor series of cos(x) about c...

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1. Determine Taylor's remainder formula (Property 2.9) for the Taylor ㅠ series of cos(x) about c = and use it to determine the following: 4 (a) What is the largest a for which the formula guarantees that the degree 4 Taylor polynomial T₁(+a) is within an error of 0.0001 4 ㅠ Give your answer rounded to two decimal places. of cos . (b) What is the smallest number of terms n in the Taylor series which TT will guarantee that the error in T+0.005) is within 0.0001 4 (ie. the size of the error must be less than 0.0001). Note that in each case we are only interested in the size of the error. ie. En (x). You must explain clearly how you can be sure that your calculated value has the required accuracy, you will be marked based on your explanation which demonstrates understanding of the use of the re- mainder formula, not purely on the numerical answers. 1. Determine Taylor's remainder formula (Property 2.9) for the Taylor ㅠ series of cos(x) about c = and use it to determine the following: 4 (a) What is the largest a for which the formula guarantees that the degree 4 Taylor polynomial T₁(+a) is within an error of 0.0001 4 ㅠ Give your answer rounded to two decimal places. of cos . (b) What is the smallest number of terms n in the Taylor series which TT will guarantee that the error in T+0.005) is within 0.0001 4 (ie. the size of the error must be less than 0.0001). Note that in each case we are only interested in the size of the error. ie. En (x). You must explain clearly how you can be sure that your calculated value has the required accuracy, you will be marked based on your explanation which demonstrates understanding of the use of the re- mainder formula, not purely on the numerical answers.

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a The Taylor remainder formula for the Taylor series of cosx about c4 is Rnx 1nx42n1 2n1 To guarante... View the full answer