Exam 2 Graded
Student
Jack Norton
Total Points
pts
Question 1
Multiple Choice pts
1.1 Local Extrema pts
− 4 pts This is a local maximum since D > 0 and fxx < 0.
1.2 Bead Integral Setup pts
− 0 pts Correct! The fourth option gives the volume of the bead.
1.3 Half a Sphere pts
− 1 pt (Second one chosen) This is only a quarter of a sphere and should not have been chosen.
− 1 pt (Third one not chosen). This gives the volume of a z ≥ 0 half sphere, so it should have been chosen.
− 1 pt (Fourth one not chosen) This gives the lower half-sphere and should have been chosen.
1.4 Change of Variables pts
− 4 pts Incorrect. The Jacobian is 1/5, so we get the second one.
Question 2
Matching pts
− 0 pts Correct! The right order is ADBC.
Question 3
Directional Derivative pts
− 1 pt Incorrect computation for directional derivative
1 Correct, but 25 + 4 = 29
Question 4
Triple Integral Setup pts
Error in Cylindrical.
− 1 pt Wrong upper θ bound.
, Question 5
Double Integral Sketch and Setup pts
− 0 pts Correct
Question 6
Student Solution Volume Under Cone pts
+ 9 pts All 7 bounds corrected appropriately in part (a), part (b) also correct
+ 8 pts 6 bounds corrected appropriately in part (a), part (b) also correct
Partial credit on part (a)
+ 1 pt Corrected dx bounds appropriately (lower bound should be -1)
+ 1 pt Corrected dy bounds appropriately (lower bound should be − 1 − x2 )
+ 1 pt Corrected dr bounds appropriately (lower bound should be 0)
+ 1 pt Corrected lower dϕ bounds appropriately (should be π/4)
+ 1 pt Corrected upper dϕ bounds appropriately (should be π/2)
+ 1 pt Corrected lower dρ bound appropriately (lower bound should be 0)
+ 1 pt Corrected upper dρ bounds appropriately (should be csc(ϕ))
Partial credit on part (b)
+ 2 pts Part(b) correct.
+ 1 pt Reasoning is good but inconsistent with work shown in part (a)
+ 0 pts Reasoning is incorrect
+ 0 pts Click here to replace this description.
+ 0 pts Blank or no correct work
Question 7
Setup with Two Integrals pts
+ 2 pts Correct!
+ 1 pt Incorrect but used dxdy order and made a good start
+ 0 pts Incorrect
Student
Jack Norton
Total Points
pts
Question 1
Multiple Choice pts
1.1 Local Extrema pts
− 4 pts This is a local maximum since D > 0 and fxx < 0.
1.2 Bead Integral Setup pts
− 0 pts Correct! The fourth option gives the volume of the bead.
1.3 Half a Sphere pts
− 1 pt (Second one chosen) This is only a quarter of a sphere and should not have been chosen.
− 1 pt (Third one not chosen). This gives the volume of a z ≥ 0 half sphere, so it should have been chosen.
− 1 pt (Fourth one not chosen) This gives the lower half-sphere and should have been chosen.
1.4 Change of Variables pts
− 4 pts Incorrect. The Jacobian is 1/5, so we get the second one.
Question 2
Matching pts
− 0 pts Correct! The right order is ADBC.
Question 3
Directional Derivative pts
− 1 pt Incorrect computation for directional derivative
1 Correct, but 25 + 4 = 29
Question 4
Triple Integral Setup pts
Error in Cylindrical.
− 1 pt Wrong upper θ bound.
, Question 5
Double Integral Sketch and Setup pts
− 0 pts Correct
Question 6
Student Solution Volume Under Cone pts
+ 9 pts All 7 bounds corrected appropriately in part (a), part (b) also correct
+ 8 pts 6 bounds corrected appropriately in part (a), part (b) also correct
Partial credit on part (a)
+ 1 pt Corrected dx bounds appropriately (lower bound should be -1)
+ 1 pt Corrected dy bounds appropriately (lower bound should be − 1 − x2 )
+ 1 pt Corrected dr bounds appropriately (lower bound should be 0)
+ 1 pt Corrected lower dϕ bounds appropriately (should be π/4)
+ 1 pt Corrected upper dϕ bounds appropriately (should be π/2)
+ 1 pt Corrected lower dρ bound appropriately (lower bound should be 0)
+ 1 pt Corrected upper dρ bounds appropriately (should be csc(ϕ))
Partial credit on part (b)
+ 2 pts Part(b) correct.
+ 1 pt Reasoning is good but inconsistent with work shown in part (a)
+ 0 pts Reasoning is incorrect
+ 0 pts Click here to replace this description.
+ 0 pts Blank or no correct work
Question 7
Setup with Two Integrals pts
+ 2 pts Correct!
+ 1 pt Incorrect but used dxdy order and made a good start
+ 0 pts Incorrect
