MATH-M 119 Study Guide - Final Guide: Riemann Sum, Coefficient, Marginal Revenue

INSTRUCTIONS: There are 15 problems on this exam, and each problem is worth 13 points, plus 5 points for writing down an approximate volume of the planet Earth in cubic miles at the bottomleft corner of page 3, for a total possible 200 points. For this exam, you are allowed to use one 8.5"X11" sheet of notes (both sides, in your own handwriting), pencil, eraser, ruler, scratch paper and calculator. Even though the questions are multiple-choice, you need to show enough work to justify your answer in order to receive full credit. After you have determined the correct solution to each problem, write the letter corresponding to your answer in the appropriate space on the right side of the page AND circle your answer. If your answer does not agree with any of the choices, after double-checking your work, choose option E) and prominently mark your answer (box, circle, underline, etc.). Time limit: Two hours. Attach (i.e. staple) any notecard and scratch paper to the rear of this exam paper. Good luck! MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. The northern third of Indiana is a rectangle measuring 96 miles by 132 miles. Thus, let D = [0, 96] times [0,132]. Assuming that the total annual snowfall (in inches), S(x,y), at (x,y) euro D is given by the function S(x,y) = 60e-0.001 (2x + y) with (x,y) euro D, find the average snowfall on D. 51.14 inches 52.06 inches 51.78 inches 52.44 inches Evaluate the work done between point 1 and point 2 for the conservative field F. Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. Evaluate the surface integral of G over the surface S. S is the portion of the cone Find the flux of the vector field F across the surface S in the indicated direction. Using the Divergence Theorem, find the outward flux of F across the boundary of the region D. Integrate the function f over the given region. f(x,y) = 1/ln x over the region bounded by the x-axis, line x = 9, and curvey y = ln x Reverse the order of integration and then evaluate the integral Use a double integral in polar coordinates to find the area of the region specified in polar coordinates. the region inside both r = 7 sin Theta and r = 7 cos Theta Use spherical coordinates to find the volume of the indicated region. the region bounded above by the sphere x2 + y2 + z2 = 25 and below by the cone z = Find the center of mass of the rectangular solid of density (x,y,z) = xyz defined by 0 LE x LE 8, Use the given transformation to evaluate the integral. where R is the parallelogram bounded by the lines y = 8x + 8, y = 8x +9, y = -6x + 2, y = -6x +7 Evaluate the line integral along the curve C. Find the work done by F over the curve in the direction of increasing t.

Directions: » You will be graded on organization, conceptual understanding, and proper mathematical communica- tion, as well as completion of the problems » Use complete sentences to communicate your thinking. Your work should be done on a separate sheet of paper. » Show as much work as you can, draw sketches if necessary and clearly explain why you are doing what you are doing » Use correct mathematical notation. Include "-" and "" where appropriate » You may work with your classmates. However, please submit your own work! » Please use this sheet as a cover page. 1. (Related Rates) A particle moves clockwise around the circle 2 +y2-16 with respect to time! 3 -2 1 o 1 3 (a) In which of the four quadrants is the derivative dy/dt positive? Explain your answer. [3 points] [4 points] (c) At what rate is the y-coordinate changing when the particle passes the point (2V2,2V2) if its x- (b) Find a relation between dx/dt and dy/dt. Show each step and explain you work. coordinate is increasing at a rate of 3 ft/sec? Explain your answer 3 points] (d) What is dx/dt when the particle is at the left-most and the right-most of the circle? That is, at (4,0) and (-4,0). Explain your answer 3 points

A carnival merry-go-round rotat D WeBWorK : CSU-MTH284-Fall18 x × C Not secure webworks2.csuohio.e U MTH284_Fall18/HW4 EigenValues_Rod/16/ Homework Sets HW4 EigenValues Rod: Problem 16 Prev Up Next HW4 EigenValues Rod Problem 16 Password/Email Result Entered 01,74 48 56 Answer Preview Grades Problems Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 The answer above is NOT correct (1 pt) 8 0.25 Let: A 27 -2 Find an invertible S and a diagonal D such that S AS-D 0 6 Preview Answers Submit Answers Your score was recorded You have attempted this problem 2 times. You received a score of 0% for this attempt. Your overall recorded score is 0% You have unlimited attempts remaining Activate Windows Go to Settings to activate Windows 10:58 PMM 12/1/20 ^

S A carnival merry-go-round rotatexWeBWork: CSU MTH284 Fall18 x+ C Not secure webworks2.csuohio.e U MTH284 Fall18/HW4 EigenValues, Rod/17/user-2699769&effectiveUser-2699769&key-vYsrs1KsSmrZ4iwgsvaFAE 1PYWi..C Homework Sets HW4 EigenValues Rod: Problem 17 Prev Up Next (1 pt) Find a 2 × 2 matrix A for which HW4 EigenValues Rod Problem 17 Password/Email Grades .5 E-spanand E span Problems Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 where Ex is the eigenspace associated with the eigenvalueA .4 Note: You can eam partial credit on this probvem. Preview Answers Submit Answers You have attempted this problem 2 times. Your overall recorded score is 0% You have unlimited attempts remaining. Email instructor Activate Windows Go to Settings to activate Windows 10:58 PMM 12/1/20 ^

S A carnival merry-go-round rotatexWeBWork: CSU MTH284 Fall18 x+ C O Not secure webworks2.csuohio.e U MTH284_Fall18/HW4 EigenValues_Rod/18/ Homework Sets HW4 EigenValues Rod: Problem 18 Prev Up Next HW4 EigenValues Rod Problem 18 Password/Email Entered Answer Preview Result incorrect Grades Problems ncorrect Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 incorrect At least one of the answers above is NOT correct (1 pt) Find a 2 x 2 matrix A such that and -5 -3 are eigenvectors of A, with eigenvalues 5 and-10 respectively. Activate Windows Go to Settings to activate Windows Note: You can eam partial credit on this probvem. 10:58 PMM 12/1/20 ^

A carnival merry-go-round rotat D WeBWorK : CSU-MTH284-Fall18 x × С Not secure I webworks2.csuohio.edu/webwork2/CSU-MTH284-Fall 18/HW4-EigenValue r-2699769&effectivelser=2699769&key=vYsrs1KsSmrZ4iwgsvaFAE 1PYWli ☆ Logged in as 2699769 Log Out MATHEMATICAL ASSOCIATION OF AMERICA MAIN MENU Courses Homework Sets webwork/csu mth284 fall18I hw4_e eigenvaluesrod 20 HW4 EigenValues Rod: Problem 20 Prev Up Next (1 pt) HW4 EigenValues Rod Problem 20 Password/Email Grades 13 10 Problems Let M 5 -2 Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Find formulas for the entries of M, where n is a positive integer An-(n-1) Mn = Note: You can eam partial credit on this problem. Preview Answers Submit Answers You have attempted this problem 1 time. Your overall recorded score is 0% You have unlimited attempts remaining. Activate Windows Go to Settings to activate Windows Email instructor CSU MTH284 Fall13/HW4 EigenValues Rod21. 10:58 PMM 12/1/20 ^

A carnival merry-go-round rotat D WeBWorK : CSU-MTH284-Fall18 x C Not secure webworks2.csuohio.e U MTH284_Fall18/HW4 EigenValues_Rod/21/ Homework Sets HW4 EigenValues Rod: Problem 21 Prev Up Next HW4 EigenValues Rod Problem 21 Password/Email Entered AC Answer Preview Grades AC Problems Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 The answer above is NOT correct (1 pt) Which of the following transformations are linear? A. D.10 Уз 2x1 Activate Windows Go to Settings to activate Windows Preview Answers Submit Answers Your score was recorded. You have attempted this problem 2 times 10:59 PMM 12/1/20 ^

S A carnival merry-go-round rotatexWeBWork: CSU MTH284 Fall18 x+ C Not secure webworks2.csuohio.e U MTH284_Fall18/HW4 EigenValues_Rod/23/ Homework Sets HW4 EigenValues Rod: Problem 23 Prev Up Next HW4 EigenValues Rod Problem 23 Password/Email Entered Answer Preview Result Grades incorret Problems incorrect Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 At least one of the answers above is NOT correct 3-6 21is a basis for IR (1 pt) The set B Find the coordinates of the vector relative to the basis B Note: You can eam partial credit on this probvem. Preview Answers Submit Answers Your score was recorded You have attempted this problem 3 times. You received a score of 0% for this attempt. Your overall recorded score is 0%. You have unlimited attempts remaining Activate Windows Go to Settings to activate Windows Email instructor 10:59 PMM 12/1/20 ^

A carnival merry-go-round rotat D WeBWorK : CSU-MTH284-Fall18 x C Not secure webworks2.csuohio.e U MTH284 Fall18/HW4 EigenValues, Rod/24/user-2699769&effectiveUser-2699769&key-vYsrs1KsSmrZ4iwgsvaFAE 1PYWi..C Homework Sets HW4 EigenValues Rod: Problem 24 Prev Up Next HW4 EigenValues Rod Problem 24 Password/Email Grades (1 pt) The vectors -2 -3 Problems Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 form a basis for R3 if and only if k38/11 Preview Answers Submit Answers You have attempted this problem 2 times. Your overall recorded score is 0% You have unlimited attempts remaining. Email instructor Activate Windows Go to Settings to activate Windows 10:59 PMM 12/1/20 ^