Lesson 19a - Integral Test Estimator

245 rn 0322 thismeansthatourerrorwillbeno

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Unformatted text preview: 2 ArcTan (k ) 4 Rn ArcTan (k ) 3 ArcTan (4) Rn ArcTan (3) 2 0.245 Rn 0.322 This means that our error will be no more than 0.322, (could possibly be as little as 0.245). Note that the integral that decides our upper bound for the error is the right hand integral. Example 2 Determine how many terms are required to have an error no more than 0.01 for the following: 1 n2 1 n 1 To guarantee an error no more than 0.01, we need our right hand integral to be smaller than 0.01. We will set it equal to 0.01 so that we can find a tight bound: n 1 ak dk Rn ak dk n 1 Rn 2 dk n k 1 Tan (1.5608) n 99.997 n Rn ArcTan (k ) n 0.01 ArcTan (n) 2 1.5608 ArcTan (n) 1.5608 ArcTan ( n) Since we know that we will always be more accurate with a larger n, we will always round up (even at 99.01) to make sure that we insure that we meet our error restriction....
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This note was uploaded on 02/07/2014 for the course MATH 1004 taught by Professor Mark during the Summer '00 term at Carleton CA.

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