MATH 241 Study Guide - Midterm Guide: Directional Derivative, Unit Vector, Krypto

12 views1 pages

turquoisegnu128

10 Jan 2019

School

University of Maryland

Department

Mathematics

Course

MATH 241

Professor

ALL

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

Document Summary

Put a box around the result of a computation: (15 points) For which unit vector u is the directional derivative duf (0, 1) greatest: (20 points) Let f (x, y) = xy + 8/(x2) + 8/(y2). The critical points of f are (2, 2) and ( 2, 2). Determine what information the second partial derivatives test gives you about f at these critical points: (25 points) Also suppose x = u2v and y = 3u + uv. What is z/ u at the point (u, v) = (1, 2): (20 points) below, determine the limit or determine it does not exist (dne).

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 241 Study Guide - Midterm Guide: Directional Derivative, Unit Vector, Krypto

Document Summary

Get access

Related textbook solutions

Calculus

Single Variable Calculus: Early Transcendentals

CALCULUS:EARLY TRANSCENDENTALS

Related Documents

MATH 241 Study Guide - Midterm Guide: Lagrange Multiplier, Directional Derivative, Maxima And Minima

MATH 241 Midterm: MATH241H_HERB-R_SPRING2007_0101_MID_SOL_1

MATH 241 Midterm: MATH241H_HERB-R_SPRING2007_0101_MID_EXAM_1

Related Questions