Let f(x) = |cos tdt ,x> 0. Then f(.x) has%3D(a) maxima when n = - 2, - 4, - 6, . . ..(b) minima when n = 0, 2, 4,|... .....(c) minima when n = 1, 3, 5, ....(d) None of these

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Answered: Let f(x) = cos t dt ,x> 0. Then Ax) has…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(part 1 of 4) Determine the value of the third derivative of f at x = 1 when f(x) 1. f"(1) 2. f" (1) 3. f(1) 4. f"(1) 5. f""(1) 1. T3 = =e 3. T3 = = = e 4. T3 e = e³ -1 -8 e³ (part 2 of 4) Determine the degree three Taylor polyno- mial centered at x = 1 for f when 3-4x f(x) 8 3! 3! e³ -3!8 e³ = 2. T3 =e7 (1 + 4(x − 1) e(5-2x) (1 - 4(x - 1) 32 + 8(x − 1)² — 33² (x − 1)²³) ¹(1. - 8(x − 1)² + 1-4x+8x² 1+ 4x − 8x² + 5. T3 =14(x − 1) 32 3²(x - 1)³) 32-2³) (3²-2-2) + 8(x − 1)² – 32 3 (x - 1)³
14) F(1) =(1, 4VF). a) Find the domain of 7(1) b) Sketch the graph of F(t). Indicate the direction of increasing t with an arrow. c) Find F'(1) d) Find F'(1) and sketch on graph at t=1
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Consider the three points (2, 2), (4,4), and (6, —2). (a) Supposed that at (2, 2), we know that fx = fy = 0 and ƒxx 0, function near the point (4,4)? ? fxy fry = 0. What can we conclude about the behavior of this (c) Supposed that at (6, -2), we know that fx = fy = 0 and fxx > 0, fyy < 0, and fxy = 0. What can we conclude about the behavior of this function near the point (6, -2)? ? Using this information, on a separate sheet of paper sketch a possible contour diagram for f.

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Let f(x) = cos t dt ,x> 0. Then Ax) has (a) maxima when n = - 2, - 4,- 6, . . . . (b) minima when n = 0, 2, 4, . . . (c) minima when n = 1, 3, 5, . %3D . . .. 13= (d) None of these