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 rm = am 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……