MATH 127 - Practice Exam 1 -Spring 2025
Name (in print):
Harish Ravichandar Nikos Gkrekas David Friedman Mark Denker
MW 11 am or 12 pm MW 1 pm or 2 pm TR 9 am TR 10 am
Sungmin Won Simon Deng Debjit Basu Jake Weaver Cheng-Pang Shih
TR 9:30 am TR 11 am TR 12 pm TR 1 pm TR 2 pm
Exam Instructions:
Date and Time: Tuesday, March 4, 2025 at 5:50-7:50pm
Calculator: Non-graphing, non-programmable, and unable to calculate limits/derivatives
• Write all of the work on this exam - nothing else will be graded. You must show your work to earn
credit. Your work must be legible and any work which you do not want graded must be scratched or
clearly crossed out. In particular, a correct answer with no work will receive little or no credit. If you
want something on the scratch paper graded for a particular problem, clearly note this. • On some
problems, you are asked to use a specific method to solve the problem. On all other problems, you
may use any method that we have covered. You may only use methods we have
not covered if you fully justify your work. Approximations may not receive credit if an algebraic
approach is possible.
• Banned Items: Devices which have or can access a camera, graphing capabilities, an internet
connection, or a computer algebra system are banned on all exams. If a proctor sees you with a
banned device during the exam, this may be classified as academic misconduct. If you must
have a banned device with you, it must be in a bag which is closed throughout the exam. • Each
student must be prepared to produce, upon request, a card with a photograph for identification.
Once you have completed the exam, find the graduate teaching assistant who teaches your
laboratory section and turn the exam in to them.
• Please act with academic integrity. The exam is out of 100 points with 7 bonus available. Good luck
on the exam!
, Formulas you may need
x = ρ sinϕ cosθ
y = ρ sinϕ sinθ
z = ρ cosϕ
True and False Questions
For each question, circle TRUE or FALSE. Selecting TRUE means that the statement is always true.
Selecting FALSE is appropriate even if the statement is sometimes true, but has a possibility of being false.
You do NOT need to justify your answer.
(1) If fx(a,b) and fy(a,b) exist, then ). TRUE FALSE
If the mixed partials exist and are continuous, then it would be true.
(2) If f(x,y) → L as (x,y) → (0,0) along every straight line through (0,0), TRUE FALSE then
lim .
This would be true if the limits were equal along every possible path (or curve) through (0,0).
(3) If f(x,y) is a continuous function, then f(x,y) must have an absolute TRUE FALSE maximum on
the disk x2 + y2 < 1
This region is bounded but not closed, so the extreme value theorem does not apply.
(4) If fx(a,b) and fy(a,b) both exist, then f is differentiable at (a,b). TRUE FALSE This is true if both
first-order partial derivatives exist and are continuous.
(5) If f(x,y) is differentiable at (a,b), then the tangent plane to f at (a,b) TRUE FALSE can
approximate values of f near (a,b).
Fill-in-the-Blank and Multiple Choice Questions
√
2
Name (in print):
Harish Ravichandar Nikos Gkrekas David Friedman Mark Denker
MW 11 am or 12 pm MW 1 pm or 2 pm TR 9 am TR 10 am
Sungmin Won Simon Deng Debjit Basu Jake Weaver Cheng-Pang Shih
TR 9:30 am TR 11 am TR 12 pm TR 1 pm TR 2 pm
Exam Instructions:
Date and Time: Tuesday, March 4, 2025 at 5:50-7:50pm
Calculator: Non-graphing, non-programmable, and unable to calculate limits/derivatives
• Write all of the work on this exam - nothing else will be graded. You must show your work to earn
credit. Your work must be legible and any work which you do not want graded must be scratched or
clearly crossed out. In particular, a correct answer with no work will receive little or no credit. If you
want something on the scratch paper graded for a particular problem, clearly note this. • On some
problems, you are asked to use a specific method to solve the problem. On all other problems, you
may use any method that we have covered. You may only use methods we have
not covered if you fully justify your work. Approximations may not receive credit if an algebraic
approach is possible.
• Banned Items: Devices which have or can access a camera, graphing capabilities, an internet
connection, or a computer algebra system are banned on all exams. If a proctor sees you with a
banned device during the exam, this may be classified as academic misconduct. If you must
have a banned device with you, it must be in a bag which is closed throughout the exam. • Each
student must be prepared to produce, upon request, a card with a photograph for identification.
Once you have completed the exam, find the graduate teaching assistant who teaches your
laboratory section and turn the exam in to them.
• Please act with academic integrity. The exam is out of 100 points with 7 bonus available. Good luck
on the exam!
, Formulas you may need
x = ρ sinϕ cosθ
y = ρ sinϕ sinθ
z = ρ cosϕ
True and False Questions
For each question, circle TRUE or FALSE. Selecting TRUE means that the statement is always true.
Selecting FALSE is appropriate even if the statement is sometimes true, but has a possibility of being false.
You do NOT need to justify your answer.
(1) If fx(a,b) and fy(a,b) exist, then ). TRUE FALSE
If the mixed partials exist and are continuous, then it would be true.
(2) If f(x,y) → L as (x,y) → (0,0) along every straight line through (0,0), TRUE FALSE then
lim .
This would be true if the limits were equal along every possible path (or curve) through (0,0).
(3) If f(x,y) is a continuous function, then f(x,y) must have an absolute TRUE FALSE maximum on
the disk x2 + y2 < 1
This region is bounded but not closed, so the extreme value theorem does not apply.
(4) If fx(a,b) and fy(a,b) both exist, then f is differentiable at (a,b). TRUE FALSE This is true if both
first-order partial derivatives exist and are continuous.
(5) If f(x,y) is differentiable at (a,b), then the tangent plane to f at (a,b) TRUE FALSE can
approximate values of f near (a,b).
Fill-in-the-Blank and Multiple Choice Questions
√
2
