University of Sargodha ADP/BS 2ed Semester (E-24) Examination 2025 Subject: CS/SE/IT Paper: Multivariable Calculus (MATH-5101)

University of Sargodha

ADP/BS 2ed Semester (E-24) Examination 2025

Subject: CS/SE/IT

Paper: Multivariable Calculus (MATH-5101)

Maximum Marks: 60

Time Allowed: 02:30 Hours

us arc bonjective parts compulory, Attempt any dire puctions from subjective part.

Objective Part

(Compulsory)

Q.1. Write short answers of the following in 2-3 lines each on your answer sheet.

Find

iz if yz - In z= x + y

Find /(3a,

a) if f(x,y) =x° + xy?

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(2*12)

її.

ili.

iv.

Evaluate: J?J, ×ye*dyax

Evaluate: C(tsin(5t))

vi.

vii.

vili.

by convolution theorem

2+x

Find the Maclaurin series for

Evaluate:

(x))

→(3,1)

ix. Use polar Coordinate to evaluate JI, * dA where R is the region inside circle.

x° + y= 9

x. Use cylindrical coordinate is find volume of the solid bounded by z = 0 and z = 4 - 12

xi.

xija Define the Fourier Sine transformation.

Subjective Part

(3*12)

02

a) Find the derivative of f(x,y,

2) = cos(xy) + ey + In(zx) at. P (1,0,-) in the direction of

U = i + 2j + 2k.

6) Find the Linearization of f(x, y,

2) = sin(a) at (211)

Find the fadius and interval of Convergence of series Enso (x + 5)", for what value of x does the

series converges.

4* Find the Maximum and Minimum values of 3x #6 subject to the constraint x+y? = 4.-

Find the volume of the region bounded by the elliptical paraboloid z = 16 - x* - y and below by the

square R : 0 ≤ x ≤ 2,0 ≤ y ≤

2.

Solve by the Method of Laplace information: 27 - 2% = 20e cost

- LK-9302/20-11-25

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