MATH 2374 Midterm: MATH 2374 UMN Spring 10 Exam 2sol

39 views4 pages

turquoisegnu128

31 Jan 2019

School

Department

Course

Professor

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

Document Summary

Second midterm: solutions: an e ective way to solve this problem is to employ the product rule formula 1 div (f curl g) = f div g + f g. In our case, take g to be equal to curl f. But the brute force approach still works pretty well here: i. =(cid:0)3y2zx 0(cid:1) i (cid:0)y3z 4xz(cid:1) j + (0 0) k. = 3y2zx i + (4xz y3z) j f curl f = (z + 1)5 3y2zx i + (z + 1)5 (4xz y3z) j. = (z + 1)5 3y2z + ( 3y2z) + 0 = 0. div (f curl f) = Y(cid:16)(z + 1)5 (4xz y3z)(cid:17) + Y(cid:16)0(cid:17: the work done by the force eld f in moving a particle along the path c is equal to the line integral. In our case, in order to set up this integral, we need to gure out rst, what force eld is acting on the particle.

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

MATH 2374 Midterm: MATH 2374 UMN Spring 10 Exam 2sol

Document Summary

Get access

Related textbook solutions

Calculus

Single Variable Calculus: Early Transcendentals

CALCULUS:EARLY TRANSCENDENTALS

Related Documents

MATH 2374 Midterm: MATH 2374 UMN Spring 08 Exam 2sol

MATH 2374 Midterm: MATH 2374 UMN Spring 07 Exam 3sol

MATH 2374 Midterm: MATH 2374 UMN Spring 09Fall

Related Questions