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A quiz question from a calculus ii course, math 106a, given in fall 2005. The question asks students to find the second-order maclaurin's polynomial for the function f(x) = sin(x^2) and to use taylor's theorem to find an upper bound for the error when approximating f(x) with m2(x) for the interval -1 ≤ x ≤ 1.
Typology: Exercises
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QUIZ 6
Show ALL your work CAREFULLY.
(a) Find the second-order Maclaurin’s polynomial M 2 (x) for the function f (x) = sin(x^2 ).
(b) Use the Taylor’s theorem to give an upper bound for the error commit- ted by using M 2 (x) to estimate f (x) for − 1 ≤ x ≤ 1. [Do your differentiation
carefully.]
Date: October 28, 2005. 1
