MATH 190 Midterm: MATH 190 Louisville Practice Exam 1 160128

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turquoisegnu128

15 Feb 2019

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For full credit show all of your work (legibly! ), unless otherwise speci ed: (10 points) answer the following questions about graphs. (a) (3 points) given the piecewise function g(x) ={ x2 2 if. 2x 5 if x > 1 x 1. , calculate the follow- ing values: g(3), g(2), g(1). (b) (4 points) for f (x) as shown on the graph, sketch the graph of its transformation g(x) = 1 (c) (3 points) determine the equation of the line through the points (1, 4) and (4, 5). Practice exam #1: (6 points) the hong kong cavaliers have 1000 fans who would come to a concert if tickets cost . Practice exam #1: (15 points) answer the following questions about the functions f (x) = 2. 3 x+6 . (e) (3 points) simplify the expression (2x3)2(3x4) (x3)4. Label which is which: (6 points) the moon is about 240,000 miles from the earth.

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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

MATH 190 Midterm: MATH 190 Louisville Practice Exam 1 160128

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