MATH V 253
MULTIVARIABLE
CALCULUS —
PRACTICE FINAL A
LATEST VERSION
WITH COMPLETE
SOLUTIONS
Study Ace Smart
APRIL 6, 2025
Page 0 of 11
, 10 marks
Multivariable Calculus — Practice Final A — 150
minutes
• The test consists of 11 pages and 9 questions worth a total of 90 marks.
• Electronic devices of any kind (including calculators, cell phones, etc.) are
forbidden.
• This is a closed book exam. No calculators, notes, or books are allowed.
• No work on this page will be marked.
• Fill in the information below before turning to the questions.
1. Let ρ(x,y,z) = px2 + y2 + z2. Find the constants a,b such that
.
Page 1 of 11
MULTIVARIABLE
CALCULUS —
PRACTICE FINAL A
LATEST VERSION
WITH COMPLETE
SOLUTIONS
Study Ace Smart
APRIL 6, 2025
Page 0 of 11
, 10 marks
Multivariable Calculus — Practice Final A — 150
minutes
• The test consists of 11 pages and 9 questions worth a total of 90 marks.
• Electronic devices of any kind (including calculators, cell phones, etc.) are
forbidden.
• This is a closed book exam. No calculators, notes, or books are allowed.
• No work on this page will be marked.
• Fill in the information below before turning to the questions.
1. Let ρ(x,y,z) = px2 + y2 + z2. Find the constants a,b such that
.
Page 1 of 11