Differential Calculus and Differential Equation 2014 – BSc Computer Science Part 1
Paper code: 13502
1502
B.sc. (Computer Science) (Part 1)
Examination, 2014
Paper No. 1.2
DIFFERENTIAL CALCULUS AND DIFFERENTIAL EQUATION
Time: Three Hours] [Maximum Marks: 50
Note: Attempt all the five questions in all section one question from each Section. All questions carry equal marks.
Section-A
1. (a) If , prove that:
(b) If , find
2. (a) Apply Maclaurin’s theorem to find the expansion in ascending powers of x of to the term containing .
(b) Expend in powers of .
Section-B
3. (a) Find the equation of the normal at the point ‘t’ on the curve:
(b) Find the length of the polar tangent and polar normal for the curve .
4. (a) Find the equation of the tangent at the point to the ellipse:
(b) If , prove that:
Section-C
5. (a) Evaluate:
(b) Evaluate:
6. (a) Show that:
(b) Evaluate:
Section-D
7. (a) Solve:
(b) Solve:
8. (a) Solve:
(b) Solve:
Section-E
9. (a) Solve:
(b) Solve:
10. (a) Solve:
(b) Solve:
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