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13 Nov 2019
MA 201-06 Final Exam Fall 2017 Version 1 1) Demonstrate that the function yex) described by the equation y- sin(rx-y) is n y = sin(nx-y) is not smooth dy dx
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Trinidad Tremblay
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Related questions
1) Demonstrate that the function y(x) described by the equation y sin(x-y) is not smooth around (1,0) (ie g does not exi h poi) by uin the formula
Question b)
..21A whore R is the ventanale with (b) A domain D is described by its bounding surfaces, along with a graph. Set up the triple integrals that give the volume of D, and find the volume of D by evaluating the indicated triple integral. . (136-9). D is bounded by the coordinate planes and z = 2-2x/3-2y. · (13.6-10). D is bounded by the planes y = 0, y 2, x = 1, z = 0 and z = (3-x)/2. . (136-11). D s bounded by the planes x 0, x 2, z -y and by z = y2/2. (c) Evaluate the triple integral. 21, (cos x sin y sin z) d: dy dx . (13.6-17). . (13.6-18 . (13.6-19). fO a+y +z) dz dy dx. fo (sin(yz)) dx dy dz.
1, 2, 4, 5
Exercises and Problems for Section 11.1 Exercises 8. A q 1. Is y = x3 a solution to the differential equation 2. Determine whether each function is a solution to the dit ,ferential equation and justify your answer: dr (a) (c) y=z4 y=x3 (b) (d) y=x4 + 3 y=7x4 9. Fil 3. Determine whether each function is a solution to the dif dy ter ferential equation and justify your answer:" 6r dx ^\ (a) y=4x3 (b) y=22,3/2 (c) y=623/2 4.. Show that y(x) = AeAz is a solution to the equation 10. Us y' = y for any value of A. on 5. Show that y = sin 2t satisfies 6 In Exe ential e dition. 11· 20 12. P dt2 6. Show that, for any constant R, the function P = Pet satisfies the equation d P 7. Use implicit differentiation to show that x2 + y2 r2 is 13. a solution to the differential equation dy/dr--/y. 14. Q Problems 15. Show that y = A + Cekt is a solution to the equation 18.
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