How can I find a range of values of x for which this approximation gives correct results rounded to 2 decimal places?

Question

How can I find a range of values of   x for which this approximation gives correct results rounded to   2 decimal places?

bluayu0y · Accepted Answer

The alternating series theorem says the truncation error is smaller than the first neglected term and of the same sign. The first term you neglect is

\frac{x^{4}}{4!}

! so we want

\frac{x^{4}}{4!} < 0.01 x^{4} < 0.24 | x | < {0.24}^{1 / 4} \approx 0.700

When you demand correct rounding to a number of places it is hard to say what the allowable error is. If you are very close to a breakpoint you may have to be very accurate. I used

0.01

as the allowable error, you can use whatever value you want.

How can I find a range of values of

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