Differential Calculus and Differential Equations 2022 – BSc Computer Science Part 1

Paper code: 13502
1502
B.Sc. (Computer Science) (Part 1)
Examination, 2022
Paper No. 1.2
Differential Calculus and Differential Equations

Time: Three Hours]

[Maximum Marks: 50

Note: Attempt five questions in all selecting one question from each Section. All questions carry equal marks.

Section-A

1. (a) If show that and .

    (b) Find when .

2. (a) Expand log(1+x) with the help of Maclavrin’s theorem.

    (b) Expand sin x in powers of (x-?/2) by Taylor’s theorem.

3. (a) Find the sub-tangent and subnormal at the point t on the cycloid.

    (b) Find the pedal equation of the parabola :

y² = 4a (x + a)

4. (a) In the curve r^m = a^m cos m? prove that :

    (b) Find the following limit :

Section-B

5. (a) Find :

    (b) Find :

6. (a) Show that :

    (b) From the definition of a definite integral as the limit of a sum evaluate:

7. (a) Solve the differential equation :

    (b) Solve the differential equation :

Section-C

8. Solve the following differential equations :

    (a)

    (b)

9. Solve the following differential equations :

    (a)

    (b)

10. (a) Solve:

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    (b) Solve:

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……End……