MATH 240 Final: MATH 240 KSU Final Exam f06

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turquoisegnu128

15 Feb 2019

School

Kansas State University

Department

Mathematics

Course

MATH 240

Professor

All

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Document Summary

Show all your work in the space provided under each question. = p (p 10)(p 1) (a) find the equilibrium points. (b) draw several trajectories. Explain your answer: find the general solution: y . Y = xy2: solve the initial value problem x + 2x + 2x = (t ) + h(t) x(0) = 0, x (0) = 0. You will need to express a part of your solution as a convolution integral involving the function h(t): find the general solution. x2y + xy . Give a lower bound for the radius of convergence of such a power series solution: (a) express ( 7, in terms of ( 1. To the mass is attached a damping mechanism with damping constant 6 kg sec. Here c and f0 are nonnegative constants. (a) suppose f0 = 0. For which values of c is the system critically damped? (b) suppose f0 = 1, c = 0.

Related Questions

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

Solve all please.