Errors in approximations Suppose you approximate f(x) = sec x at the points x = -0.2, –0.1, 0.0, 0.1, 0.2 using the Taylor polynomials p,(x) = 1 + x²/2 and P.(x) = 1+ x²/2 + 5x*/24. Assume the exact value of sec x is given by a calculator. a. Complete the table showing the absolute errors in the approxi- mations at each point. Show three significant digits. b. In each error column, how do the errors vary with x? For what values of x are the errors largest and smallest in magnitude? * Isecx - P.(r)| Isecr - P.(r)| |sec x - P.(x)| -0.2 -0.1 0.0 0.1 0.2 f(x) = e, P1(x) = 1 – x, p,(x) = 1 - x + 2

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