University of Sargodha ADP/BS 1st Semester Examination 2025 Subject: CS/IT/SE Paper: Calculus & Analytic Geometry (URCO-5102/URCO-5103) Time Allowed: 02:30 Hours

University of Sargodha

ADP/BS 1st Semester Examination 2025

Subject: CS/IT/SE Paper: Calculus & Analytic Geometry (URCO-5102/URCO-5103)

Time Allowed: 02:30 Hours

Maximum Marks: 60

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

Objective Part

(Compulsory)

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

(2*12)

i. Find lim *° +2x'-1

x→-2 5-3x

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

ili.

Find the point on the curve y = x4 - 6x2 + 4 where the tangent line is horizontal.

iv.

Iff (t) = eat sin bt, find f'(t).

V:

Find -

X+1

ax v

vi.

Define the increasing function.

vii.

Evaluate 53(2x+4) ax.

viii.

Find the equation of the normal line to the curvey =x - 3x + 2 at x =

1.

ix.

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

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

x.

xi.

X11.

Find - In(sin x).

Determine the domain of a function f(x) = =x2-x

Evaluate S cose

sin2 e

de.

Q.2.

Q.3.

Q.4.

Q.5.

Q.6.

Subjective Part

(3*12)

Solve the inequality |x - 3| + |x + 2| <

11.

Find y"ifx*+y* =

16.

Find the absolute maximum and absolute minimum values of f(x) = 2x3 - 3x2 - 12x + 1, [-2,3].

Find SV1+x*x° dx.

Find the area of the region enclosed by the parabolas y = x* and y = 2x - x.

- LK-5093,6183/30-04-25 -