Question
Asked Nov 2, 2019
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How many terms are needed in series of cos x to compute for |x| < (1/2) accurate to 1/2 decimal places(rounded)?

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Expert Answer

Step 1

The (minimum) number of terms needed to compute the values with maximum error =0.1,0.01

Step 2

Standard error formula in Taylor series expansion applied to the given function

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Taylor series about 0 (-1)(-1)2-1) 2(n-1) f(x)= cosx 1- 2! 4! Maximum error Maxf(x) x max xover [0.0.5] (n+1)! 0.5 (as f(x)1, Vn) (n+1)!

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Step 3

number of terms needed to control the ...

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1)max error 0.1, 0.5 0.1 (n+1)!5 (n+1)! smallest value of n 2 So, 2 terms needed

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