Errors and approximation

[chb1980]

hi how are you ?

i have no idea to get it..please help me


Xa=3.14 and Ya=2.685 are correctly rounded to the numbers of digits shown.
Estimate the errors in the function value sin(XaYa) in terms of the errors in Xa and Ya . Bound the relative errors.

thanks

[r035198x]

hi how are you ?

i have no idea to get it..please help me


Xa=3.14 and Ya=2.685 are correctly rounded to the numbers of digits shown.
Estimate the errors in the function value sin(XaYa) in terms of the errors in Xa and Ya . Bound the relative errors.

thanks

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P.S Changed thread title.

[emaghero]

hi how are you ?

i have no idea to get it..please help me


Xa=3.14 and Ya=2.685 are correctly rounded to the numbers of digits shown.
Estimate the errors in the function value sin(XaYa) in terms of the errors in Xa and Ya . Bound the relative errors.

thanks

Evaluate the Taylor Series of the function f(x) = Sin(x). Google it to find out how or check the link I gave below. The Taylor Series gives an accurate approximation to the function and you also get a bound for the error in the approximation. The series can be coded in C++ as can the error approximation. The more terms you take in the series the better the approximation. A good place to start learning about Taylor Series is any Calculus text book you can get your hands on, otherwise I'd say take a look at the following link:

http://mathworld.wolfr am.com/TaylorSeries.ht ml

Remember, if you want an order n approximation to the function the error is given by the (n+1)st term.

Happy Trails

emaghero