MAC 2311 Midterm: MAC2311 S97 Test 4

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turquoisegnu128

31 Jan 2019

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Calculus 1 final exam b april 28, 1997. Instructions: do not write your answers on this paper, use separate answer sheets. To receive credit, you must show all work. You are not required to simplify your answers: (10 pts. ) Graph the equation y 10 = 2(x 2)2. A population triples in size every 15 days. Do not round o leave your answer in terms of logarithms: (10 pts. ) For the graph below, give a function whose graph best matches the one given. y. Express the function w(x) = as a composition of the following functions. Use as many functions from the list as possible. f (x) = x g(x) = x2. The gure below is the graph of y = f (x). Sketch the graph of y = f (x). h(x) = x 4 j(x) = 3x k(x) = 1 y = f (x) x: (10 pts. )

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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

MAC 2311 Midterm: MAC2311 S97 Test 4

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