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Unformatted text preview: adams (bda255) – HW15 – Radin – (56635) 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Use the Taylor series representation cen- tered at the origin for e − x 2 to evaluate the definite integral I = integraldisplay 5 6 e − x 2 dx. 1. I = n summationdisplay k = 0 1 k !(2 k + 1) 6 · 5 2 k +1 2. I = ∞ summationdisplay k = 0 (- 1) k k ! 6 · 5 2 k 3. I = ∞ summationdisplay k = 0 1 k ! 6 · 5 2 k 4. I = ∞ summationdisplay k = 0 (- 1) k 2 k + 1 6 · 5 2 k +1 5. I = ∞ summationdisplay k = 0 (- 1) k k !(2 k + 1) 6 · 5 2 k +1 002 (part 1 of 4) 10.0 points Suppose p 4 ( x ) = 3- 5 x + 4 x 2- 5 x 3 + 2 x 4 is the degree 4 Taylor polynomial centered at x = 0 for some function f . (i) What is the value of f (0)? 1. f (0) = 4 2. f (0) = 5 3. f (0) =- 4 4. f (0) = 3 5. f (0) =- 3 003 (part 2 of 4) 10.0 points (ii) What is the value of f (3) (0)? 1. f (3) (0) =- 5 2. f (3) (0) =- 30 3. f (3) (0) = 30 4. f (3) (0) =- 5 3 5. f (3) (0) = 5 3 004 (part 3 of 4) 10.0 points (iii) Use p 4 to estimate the value of f (0...
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