MA 126 Final: 2-11s-Final exam

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turquoisegnu128

31 Jan 2019

School

UAB

Department

MA-Mathematics Courses

Course

MA 126

Professor

All

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Show all your work and give reasons for your answers. Good luck! (1) (5 points) find the angle between the vectors < 3, 2, 0 > and < 1, 1, 2 >. Name: (2) (5 points) find the parametric equation of the line perpendicular to the plane. 3x y + 4z = 5 through the point ( 1, 2, 3). 3+ x x dx. (6) (5 points) evaluate r x sin(x) dx. 3 (7) (5 points) express f (x) = x. Also state the interval of conver- (8) (5 points) use series to approximate cos( 1 not need to add the terms in the sum. ] 10 ) with an error less than 10 6. 4 (9) (5 points) evaluate r sin3(x) dx. (10) (5 points) find the interval and radius of convergence of the power series p n=0 (cid:0) x. 3 (cid:1)n. (11) evaluate the following integrals: (a) (6 points) r sin( x)

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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

MA 126 Final: 2-11s-Final exam

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