Question: Show that Hence derive a polynomial approximation to (1 x) 1 with an error that, in modulus, is less than 0.5 10 4 for
Show that
Hence derive a polynomial approximation to (1 – x)–1 with an error that, in modulus, is less than 0.5 ×10–4 for 0 ≤ x ≤ 0.25. Using nested multiplication, calculate from your approximation the reciprocal of 0.84 to 4dp, and compare your answer with the value given by your calculator. How many multiplications are needed in this case?
1 1- x = 1 + x + x + ... + x- + xn 1- x (x + 1)
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