MTH301 Final Term Past Papers File 1 Set 2

FINALTERM EXAMINATION

SPRING 2006

MTH301 - CALCULUS II (Session - 2 ) Marks: 55

Time: 120min

Student Name:

Center Name/Code:

Exam Date: Thursday, August 17, 2006

3. Calculator is allowed.

Question

Question Marks

Q1. Laplace transform of ‘t ‘ is (2 marks)

s

s

s e

s

Q2. Symmetric equation for the line through (1,3,5) and (2,-2,3) is (2 marks)

y z x

y z x

y z x

y z x

Q3. The level curves of f(x, y) = y Cscx are parabolas. (1 marks)

True.

False.

Q4. The equation (1 marks)

z r is written in

Rectangular coordinates Cylindrical coordinates

Spherical coordinates

None of the above

Q5. Compute (5 marks)

C ds x

where C is the curve , 0 x t y t t

Q6. Evaluate (5 marks)

(3 2 , 1 , Q x y z dV over the box x y z

Q7. Use Stokes theorem to evaluate the integral (10 marks)

C F dr

where F z i x j y k C is the circle x y

In the xy-plane with counter clockwise orientation looking down the positive z-axis.

Q8. Find (3 marks)

wwx f for function wz f w x y z w xyz e

Q9. Locate critical points for the function (4 marks)

0 , 0) a b f x y xy a b x y

Q10. Set up a double integral for the volume bounded by surface (4 marks)

z= x y y x

and first