MTH 286 Midterm: MTH 286 Cleveland State Test1sol

173 views6 pages

turquoisegnu128

15 Feb 2019

School

Department

Course

Professor

For unlimited access to Study Guides, a Grade+ subscription is required.

Document Summary

Write your name on the back of your test. 1. (10) use the guess and test method to solve the second order di erential equation initial value problem: d2y dt2 + 6 dy dt. + 8y = 0, y(0) = 2, y (0) = 1. Solution: we try the solution y1(t) = est. Substituting in to the di erential equation: s2est + 6sest + 8est = 0 (s2 + 6s + 8)est = 0 s2 + 6s + 8 = 0 (s + 4)(s + 2) = 0. We have solutions of the form y(t) = ae 2t + be 4t where a and b are constants that depend on the initial conditions. From the initial conditions, y(0) = 2 = a + b y (0) = 1 = 2a 4b. To check that this solution is correct, we di erentiate it and substitute it in to the original di erential equation: y (t) = 7e 2t.

Related Questions

question 23 please

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

Answer #44 question with steps and explanation to solution

MTH 286 Midterm: MTH 286 Cleveland State Test1sol

Document Summary

Get access

Related Documents

MTH 286 Midterm: MTH 286 Cleveland State Test1s02

MTH 286 Midterm: MTH 286 Cleveland State Test2msol

MTH 286 Final: MTH 286 Cleveland State pracFinalsol

Related Questions