Paper code: 13502
B.sc. (Computer Science) (Part 1)
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.
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 .
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:
5. (a) Evaluate:
6. (a) Show that:
7. (a) Solve:
8. (a) Solve:
9. (a) Solve:
10. (a) Solve: