### Recent Question/Assignment

1 Assignment 2 
Instructions:
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 

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 

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 

Convert the integral

to polar coordinates.
Question 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 

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 

Convert the integral

to spherical coordinates.
1