URCE 5102 ADP/BS 1 Semester/Term University Of Sargodha (UOS) 2025

University of Sarsogpy

: ADP/BS 15 Semester Examination 2025

Subject: CSAT/SE Paper: Calculus & Analytic Geomet URCQ-5102/URCQ-5103

. Time Allowed: 02:30 Hours Maximum Marks: 60

Note: Objective part is compulsory. Attempt any three questions from subjective part.

Objective Part (Compulsory)

: Lt i h Ee Shen (2*12)

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

2

it Bindi ZHEEL

x--2 5-3x

ii. Determine whether f(x) = x5 + x is even or odd. 45

iii. Find the point on the curve y = x* — 6x2 + 4 where the tangent line is horizontal.

iv. If f(t) = e* sin bt, find f'(t).

Vi Find Lau

dx \x—2

vi. Define the increasing function.

be 3 1 :

vii. Evaluate [; (2x + o) dx.

viii. Find the equation of the normal line to the curve yl=1%2 —3x+ 2 atx =

1.

ix. The velocity of a moving object is given by v(t) =4t +2. Find the total distance traveled from ¢ = 0

to t = 5 by calculating the area under the curve,

aly be :

x. Find = In(sin x).

xi. Determine the domain of a function f(x) = ——.

xii. Evaluate [ S22 d6.

Subjective Part 3*12)

Q.2. Solve the inequality [x — 3| + |x + 2| <

11.

Q.3. Find y" ifx* + y* =

16. 5

Q.4. Find the absolute maximum and absolute minimum values of

76) = 208 =p 12% +1 [—

Q.5. Find [V1 +x? x5 dx. [=23].

Q.6. Find the area of the region enclosed by the parabolas y = x2 44 P= Dor 1

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