Multivariable Calculus 3 Semester/Term UOG — University of Gujrat 2024
Discussion
Ask a question about this paper, or help someone else with theirs. Answers are emailed to whoever asked.
No questions yet — be the first to ask.
Need Paper?
See all →
Need a paper or stuck on a question? Ask here — students reply and you get an email.
Ask about a paper-
BS ZOOLOGY first semester Animal diversity ZOOL 101 - university of Punjab 2025
0 replies Reply → -
Literary criticism
1 reply Reply → -
this paper consists of 60 marks but now we have 35 marks paper.
1 reply Reply → -
Can you please tell me more past papers please because my exams are starting from next week
1 reply Reply → -
Did you provide the past papers of the science of society uos?
1 reply Reply →
More Multivariable Calculus papers
See all
Multivariable Calculus BS/MPhil Computer Science/MS Computer Science 5 Semester/Term UOS — University of Sargodha 2025
Uploaded 2 days ago · by Hifza
Download ↓
Multivariable Calculus ADS/MS Computer Science/MSc Computer Science 4 Semester/Term PU — University of the Punjab 2022
Uploaded 2 days ago · by Hifza
Download ↓
Multivariable Calculus BS 5 Semester/Term UOS — University of Sargodha 2024
Uploaded 4 days ago · by Aziz Bhatti
Download ↓
Multivariable Calculus ADP/BS 2 Semester/Term UOS — University of Sargodha 2025
Uploaded 5 days ago
Download ↓
Multivariable Calculus ADP/BS/BSCS/BSSE/BSSE/CS/IT/BSIT 2 Semester/Term UOS — University of Sargodha 2025
Uploaded 19 days ago
Download ↓
Paper text
UNIVERSITY OF GUJRAT
Final Term Examination
FALL -2024
Course Code: MATH-110 Course Title: Multivariable Calculus
SECTION A
Q. 1. Solve the following short questions: 4x5 = 20 Marks
a. Find all 2nd order partial derivatives of the function: f(x, y) = ax sin(x + y).
b. Show that Wxy = Wyx, i.e W(x, y) = ln(2t + 3x).
c. Find the Laplace transformation of the function: f(t) = Sinat Cosht.
d. Solve the limit lim (x,y)->(1,1) sin(x^2-y^2) / x^2-y^2
SECTION B
Attempt long questions any two out of three: 2x15 = 30 Marks
Q. 2: Find Fourier representation of:
f(x) = { pi-x, 0 < x < pi
{ 0, pi < x < 2pi
and has a period 2pi.
Q. 3: State and prove Green's theorem.
Q. 4: Find the tangent plane and normal line to the surface x^2 + y^2 + z^2 = 3; at the point P(1, 1, 1).
SECTION C
Attempt long question any one out of two: 1x10 = 10 Marks
Q. 5: Determine half-range Fourier sine series for f(x) = x^2, in 0 < x < pi.
OR
Q. 6: Evaluate the surface integral ff yds where S is the surface
z = x + y^2, 0 <= x <= 1, 0 <= y <= 2
