MAT 132 Midterm: MAT 132 SBU Exam Midterm I132 s10 Solution

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turquoisegnu128

31 Jan 2019

School

Stony Brook University

Department

Mathematics

Course

MAT 132

Professor

All

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MAT 132 Full Course Notes

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Solutions to midterm i for mat 132 (spring. Instructions: print your name, id number and section number below. Do each of the following 6 problems in the spaces provided. Show some work or give an explanation where you are asked to do so. It is not necessary to simplify your answers. Please do not use calculators or any other electronic devices, notes or books during the exam time. (1) (30 points) compute the following inde nite integrals. (a) r (x2 + 1. Solution: subsitute u = sin(x) and du = cos(x)dx. Solution: use the trig identity sin2( 2x) = 1 cos2( 2x) and the substitution u = cos( 2x), du = 2sin( 2x). Z sin3( 2x)dx = z (1 cos2( 2x))sin( 2x)dx = cos3( 2x) cos( 2x) du) = (u . 1 x + 1 (x + 2)(x + 4) dx (b) (show some work) evaluate the de nite integral of part (a).

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can anyone do number 3 for me please. i'll give 5 stars

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 132 Midterm: MAT 132 SBU Exam Midterm I132 s10 Solution

MAT 132 Full Course Notes

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