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(1 point) Get help entering answers See a similar example(.PDF) Assume that f is

ID: 2886557 • Letter: #

Question

(1 point) Get help entering answers See a similar example(.PDF) Assume that f is a function with |f (a) 12, for all n and all real r. Let T, (x) denote the Taylor polynomial of degree n for f(x) about the point 0 What is the least integer n for which you can be sure that In places, i.e., so that the absolute error | Rn Lagrange form of the Remainder, evaluated at approximates accurately to 3 decimal | is less than 0.0005 ? Here K. denotes the 104 What is the least integer n for which you can be sure that Tn (1) approximates f (1) accurately to 3 decimal places? What is the least integer n for which you can be sure that In(2) approximates f (2) accurately to 3 decimal places?

Explanation / Answer

Maximum value is 12 (given).

Since error bound is 0.0005, set up as

12*(0.5)^(n+1)/(n+1)! <0.0005

Here n is an integer, try with n=1,2,3.... so that above inequilaty holds true.

n=5

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Maximum value is 12 (given).

Since error bound is 0.0005, set up as

12*(1)^(n+1)/(n+1)! <0.0005

Here n is an integer, try with n=1,2,3.... so that above inequilaty holds true.

n=7

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ince error bound is 0.0005, set up as

12*(2)^(n+1)/(n+1)! <0.0005

Here n is an integer, try with n=1,2,3.... so that above inequilaty holds true.

n=11