MATH 551 Final: MATH 551 KSU Final Exam f02

12 views14 pages

turquoisegnu128

15 Feb 2019

School

Kansas State University

Department

Mathematics

Course

MATH 551

Professor

All

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

Document Summary

Show all your work in the space provided under each question. Each problem is worth 10 points except for problem 14 which is worth 20 points: find the coordinates of the vector . Of r3: given a = . 1 3 0(cid:21): find a basis for the nullspace of the matrix a = (cid:20)1 3 2 page 3 of 14, use the gram-schmidt process to nd an orthogonal basis for the subspace of page 4 of 14. Although it is easy to guess the answer, you will receive credit only if you show the steps of the gram-schmidt process: compute det a where a = 1 1 1 1 page 5 of 14: de ne t : r3 r4 by t v = av where a = Find a basis for the image of t and a basis for the nullspace of t . page 6 of 14.

Related Questions

Full step-by-step solutions will be chosen.

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 551 Final: MATH 551 KSU Final Exam f02

Document Summary

Get access

Related textbook solutions

Calculus

Single Variable Calculus: Early Transcendentals

CALCULUS:EARLY TRANSCENDENTALS

Related Documents

MATH 551 Midterm: MATH 551 KSU Test 2f02

MATH 551 Final: MATH 551 KSU Final Exam s01

MATH 551 Final: MATH 551 KSU Final Exam s03

Related Questions