Differential Calculus and Differential Equation 2017 – BSc Computer Science Part 1

Paper code: 13502
1502
B.sc. (Computer Science) (Part 1)
Examination, 2017
Paper No. 1.2
DIFFERENTIAL CALCULUS AND DIFFERENTIAL EQUATION

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) Find nth differential coefiicient of .

    (b) If and , show that :

2. (a) If , prove that :

    (b) State and prove Taylor’s theorem.

3. (a) Evaluate :

    (b) Show that the Pedal equation of the ellipse is:

4. (a) Show that the locus of the extremily of the polar subnormal of the curve is .
    (b) Find the polar sub-tangent of the ellipse :

Section-B

5. (a) Solve the following :

    (b) Solve the following :

6. (a) Solve the following :

    (b) Solve the following :

7. (a) Solve the following :

    (b) Solve the following :

Section-C

8. (a) Solve:

    (b) Evaluate the following :

9. (a) Evaluate the following :

      (b) Evaluate as the limit of a sum.

10. (a) Find the indefinite integral :

      (b) Evaluate the following :

……End……