(1 point) Let P₂(x) be the second-order Taylor polynomial for cos x centered at x = 0. Suppose that P₂(x) is used to app

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1 Point Let P X Be The Second Order Taylor Polynomial For Cos X Centered At X 0 Suppose That P X Is Used To App 1 (50.63 KiB) Viewed 58 times

(1 point) Let P₂(x) be the second-order Taylor polynomial for cos x centered at x = 0. Suppose that P₂(x) is used to approximate cos x for x < 0.2. The error in this approximation is the absolute value of the difference between the actual value and the approximation. That is, Error = |P₂(x) - cosx. Use the Taylor series remainder estimate to bound the error in the approximation. Your answer should be a number; that is, you should give a bound for the error which works for all in the given interval. Hint: Notice that the second- and third-order Taylor polynomials are the same. So you could think of your approximation of cos x as a second-order approximation OR a third-order approximation. Which one gives you a better bound? Error < Use the alternating series remainder estimate to bound the error in the approximation. Your answer should be a number; that is, give bound for the error which works for all in the given interval. Error < In either case, will the actual value of cos a be bigger or smaller than the approximated value, assuming a 0? Bigger ? Bigger Smaller Depends on value of x Note: In order to get credit for this problem all answers must be correct. Preview My Answers Submit Answers