Use four decimal digit arithmetic with rounding to evaluate the function g{x) =

Question

Use four decimal digit arithmetic with rounding to evaluate the function g{x) = (x+1)1/3 - 1 at x = 0.001. (In other words, after every arithmetic operation, Lie calculated value is rounded to four decimal digits where numbers arc assumed to be of the form 0.d1d2d3d4 x10m for m an integer and with d1 0). Why would v/e not expect the evaluated value to be very accurate? Let omega be a real number. Use the result omega -1 = omega 3 -1/1+ omega + omega2 to suggest an alternative expression for the g(x) of part (a) which would be more accurate for its evaluation when y is near 0. Use your alternative expression to calculate g(0.00 1), again using four decimal digit arithmetic with rounding. Use your p3 of Question 1(a), again using four decimal digit arithmetic with rounding, to approximate g(0.001). Compare this approximation with the one calculated in part (b).

Explanation / Answer

use g(0)=0 and then tailor s formula about the centre zero with radius .0001

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