How can Taylor Series help us find a value of h for a specific error tolerance?

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SUMMARY

The discussion focuses on using Taylor Series to determine a value of h such that for |x| PREREQUISITES

  • Understanding of Taylor Series expansion
  • Familiarity with the sine function and its derivatives
  • Knowledge of error analysis in numerical methods
  • Ability to manipulate inequalities and absolute values
NEXT STEPS
  • Research the Lagrange form of the remainder in Taylor Series
  • Study the convergence criteria for Taylor Series approximations
  • Explore error bounds for polynomial approximations of functions
  • Learn about numerical methods for estimating function values
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Students and professionals in mathematics, particularly those studying calculus and numerical analysis, as well as anyone interested in approximation methods for functions.

HappyN
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how would you use Taylor Series to answer this:
Find a value of h such that for |x|<h implies sin(x)=x-x^3/6 +x^5/120 + R where |R|< 10^-4?
 
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HappyN said:
how would you use Taylor Series to answer this:
Find a value of h such that for |x|<h implies sin(x)=x-x^3/6 +x^5/120 + R where |R|< 10^-4?

Well, those are the first thre terms of the series for sinx (∑ (-x)2n+1/(2n+1)!) …

so what formula do you know for the remainder? :smile:
 
What formula should we know for the remainder?? Am stuck at this point..
 

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