MA 125 Midterm: MA_125_15-Spring_test_4 Spring 2015

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turquoisegnu128

31 Jan 2019

School

UAB

Department

MA-Mathematics Courses

Course

MA 125

Professor

All

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Show all your work and justify your answer! No partial credit will be given for the answer only! All problems in part i are 8 points each: given the graph of the function y = f (x) below, estimate (a) f (2), (b) f 1(1. 6), (c) (f 1) (1. 6). y. 2: if f (x) = ln(sin(x)), nd f (x, if f (x) = ex. 5x, nd all critical numbers of f (x) (if any): evaluate z ln(x) x dx. 3: solve e1 x = 10, solve ln(1 x) = 10, let f (x) = x5 + x 7 = 0. Newton"s method, if the rst approximate solution is x1 = 1. 2. 4: use the graph below to draw the location of second approximate solution given that the rst approximate solution x1 = 1. 5 as indicated. Label the value of x2 in the picture. y.

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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

MA 125 Midterm: MA_125_15-Spring_test_4 Spring 2015

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