Question: For IEEE double precision floating point arithmetic, a unit roundoff is approximately 2.2*10^-6. Suppose that for small x, the relative error in the computed value

For IEEE double precision floating point arithmetic, a unit roundoff is approximately 2.2*10^-6.

Suppose that for small x, the relative error in the computed value of sin x is approximately unit roundoff. then what is the relative error in x-sinx? For what value of x do we expect the relative error in x-sinx to reach 100%? [Note: x-sinx is approximately equal to x^3/6 for small x]

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