1 Assignment 2 [20]

Instructions:

Please answer the questions carefully, and clearly write your student number and name.

When uploading your assignment, upload the document as a pdf.

When saving your document, please save the file with your students number then name (such as ”201912345-JohnPaul.pdf”).

Note that the deadline to submit the assignment is 08:00 on Friday 29 May 2020.

Question 1 [4]

Use Lagrange multipliers to find the point (a,b) on the graph of y = e6x, where the value of ab is as small as possible.

Question 2 [4]

Let f(x,y) = x2ex2 and let R be the triangle bounded by the lines x = 4, x = y/2, and y = x in the xy-plane. Express RR f dA as a double integral in two different ways (dxdy and dy dx), then evaluate one of your integrals to find the value of RR f dA.

Question 3 [2]

Convert the integral

to polar coordinates.

Question 4 [4]

Find the volume of the solid in R3 bounded by y = x2, x = y2, z = x + y + 24 and z = 0.

(Show calculations)

Question 5 [3]

Set up the integral RRRW f(x,y,z)dV for the function f(x,y,z) = z and region x2 + y2 = z = 49 in cylindrical coordinates.

Question 6 [3]

Convert the integral

to spherical coordinates.

1

Instructions:

Please answer the questions carefully, and clearly write your student number and name.

When uploading your assignment, upload the document as a pdf.

When saving your document, please save the file with your students number then name (such as ”201912345-JohnPaul.pdf”).

Note that the deadline to submit the assignment is 08:00 on Friday 29 May 2020.

Question 1 [4]

Use Lagrange multipliers to find the point (a,b) on the graph of y = e6x, where the value of ab is as small as possible.

Question 2 [4]

Let f(x,y) = x2ex2 and let R be the triangle bounded by the lines x = 4, x = y/2, and y = x in the xy-plane. Express RR f dA as a double integral in two different ways (dxdy and dy dx), then evaluate one of your integrals to find the value of RR f dA.

Question 3 [2]

Convert the integral

to polar coordinates.

Question 4 [4]

Find the volume of the solid in R3 bounded by y = x2, x = y2, z = x + y + 24 and z = 0.

(Show calculations)

Question 5 [3]

Set up the integral RRRW f(x,y,z)dV for the function f(x,y,z) = z and region x2 + y2 = z = 49 in cylindrical coordinates.

Question 6 [3]

Convert the integral

to spherical coordinates.

1

ASSESSMENT BRIEFSubject Code and Title PROJ6003 Project Execution and ControlAssessment Assessment 1: Change Management (2 parts)Part A: Module 1-2 Discussion ForumPart B: Change ControlIndividual/Group...Assessment 1 Part Bproject schedule needs to be done using projectlibreand creating WBS using any format powerpoint,excell..etc but not very fancy.then 1500 descriptionplease read and follow the case study...1 - Identify at least two best practice principles for each of the 4 management functions of Hanning, Organising, trading, and Controlling2 Select an engineermg company (or one with engineering focus)...Business Ethics and Sustainability Assessment 2 BriefAssessment task 2: Individual Case Study Analysis and Report Objective(s): This addresses subject learning objective(s): 1, 2, 3 and 4 Weight: 50%Due:...I will provide the exact problem which needs to be solved. Please let me know if you have an expert on this subject.49325 CAMD: Computer-Aided Mechanical DesignProject (2020 SPR Semester)Group: Students...you just need to answer all of the questions.Macroeconomics 1ECON1010Semester 2, 2020Assignment 3Student Name:Student Number:Tutorial Group:Tutorial Day & Time:Tutor’s Name:Task 1Writing material for...ITNE3007 Advanced RoutingProjectAssignment Type Group Project (4 students in each group)Week Issued 7Total Marks 20Submission Deadline Week 12 (25-October-2020) via MoodleSubmission files Only one submission...**Show All Questions**