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The following table contains the evaluation of the Taylor polynomial centered at a = 1 for f(x) = 1/ x . What is the degree of this polynomial? x T(x) 0.5 1.88 0.6 1.62 1.8 0.33 2.9 -4.15 3 -5.00. 2 3 1. 1. 2. 3.

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  1. The following table contains the evaluation of the Taylor polynomial centered at a = 1 for f(x) = 1/x. What is the degree of this polynomial? x T(x)0.5 1.88 0.6 1.62 1.8 0.33 2.9 -4.15 3 -5.00 • 2 • 3 • 1

  2. 1. 2. 3. Find the Taylor polynomial {image} for the function f at the number a = 0. {image} • {image} • {image} • {image}

  3. Use Taylor's Inequality to estimate the accuracy |R3| of the approximation f(x) at the number a = 0, when {image} {image} • 0.5001 • 0.0001 • 1.0001

  4. Use the Alternating Series Estimation Theorem or Taylor's Inequality to estimate the range of values of x for which the given approximation is accurate to within the stated error. {image} • -1.092< x < 1.492 • -0.792< x < 1.792 • -1.292 < x < 1.292

  5. A car is moving with speed 25 m/s and acceleration 2m/s2 at a given instant. Using a second-degree Taylor polynomial, estimate how far the car moves in the next second. • 26 m • 26.5 m • 27 m

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