MAT-2130 Final: MATH 2130 App State Fall2016 Final Exam answer key

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turquoisegnu128

15 Feb 2019

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Name: x = cos( ) sin( ) y = sin( ) sin( ) z = 2 (1 + cos(2 ): (15 points) a few vector elds. (a) the following are plots of several vector elds. Please note that all of the vectors have been scaled down so they do not overlap each other. Write a, b, and c next to the appropriate vector eld"s formula. Put an x next to the formula whose vector eld is not shown. Circle yes or no . (b) compute the divergence and curl of f(x, y, z) = hx3y2z, xz2 + y, z5i. [warning: one of the following integrals below will have to be split into 2 pieces. ] (a) set up the integral rrr x e x2+y2. [don"t evaluate the integral. ] da using the order of integration dy dx . (b) set up the integral rrr x e x2+y2.

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1. (45 marks) Short-Answer Questions. Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal difficulty. Full marks will be given for correct answers placed in the box, but at most 1 mark will be given for incorrect answer. Unless otherwise stated, it is not necessary to simplify your answers in this question. a) Find the equation of the tangent plane to the graph of the function z = f(x,y) = sell at (0,1). Answer b) Evaluate (T, 0) if f(x,y) = sin(ry). Answer c) Graph of a function z = f(x,y) is given by: Which of the following level curves correspondes to this function. Answer d) If f(x,y) = e(3x – 2y), find lim - Math)-f(x,y) e) Find % if f(x, y) = x2 - y3 and 2 = r sin(t), y = r cos(t). Answer f) Evaluate the directional derivative of f(x, y) = !at (1, -1) in the direction of u =(2, 1). Answer 8) Does Simono converge? h) Sketch the direction field of the differential equation = 1-2y. i) Consider the differential equation ay = 15 - 31, y(0) = 0, and use Euler's method with step size 0.1 to estimate y(0.1). Answer j) Knowing that (-3,-3) is a critical point of f(x,y) = 2:3 + y2 – 4.cy -3.0, use the second derivative test to find out whether it is a local minimum, local maximum, or a saddle point. Answer k) Solve the initial value problem, dy dt 642 2y + cos(u) y(1) = . Answer 1) Is ū=(2,2, -1) perpendicular to v = (5,-4, 2)? Answer m) Find the area between the graph of y = 1 + sin(x) and y=1-sin(x) from 0 to 7. Answer n) Determine the lentgh of the curve y = 8/2,0 SIS 3. Evaluate and simplify your answer. Answer o) Express the volume of the solid obtained by rotating the bounded region that lies between curves y = (x-2)2 and y=1,150 $4 about the vertical line 2 = 5. Do not evaluate this integral. Answer

MAT-2130 Final: MATH 2130 App State Fall2016 Final Exam answer key

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