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The sine function is given by the infinite series sin(x) = x - x3/3! + x5/5! + x7/7! + ... a) What are the forward and backward errors if we approximate the sine function by using only the first term in the series, for x = 0.1, 0.5, 1.0? b) Using the first two terms.

With exact rounding, we know that each elementary operation has a relative error which is bounded in terms of the rounding unit n; e.g., for two foating point numbers x and y, (x + y) = (x + y)(1 + E); |E| <= n. But does a similar result hold for elementary functions such as sin, ln and...