MTH301 Midterm Past Paper Spring 2006

VUSR · MTH301 Calculus II · Mid Term Examination – Spring 2006 · Time Allowed: 90 Minutes · Please · read · the · following · instructions · carefully before attempting any of the questions:

question.

examination from anyone. a. If you think that there is something wrong with any of the questions, attempt it to the best of your understanding. b. If you believe that some essential piece of information is missing, make an appropriate assumption and use it to solve the problem.

marks. 3. Calculator is allowed.

**WARNING: Please note that Virtual University takes serious note of

unfair means. Anyone found involved in cheating will get an `F` grade in

this course.

Q1. Marks : 5

in the Find the directional derivative D fu(1, 1,1) of direction of u = -�( 1, 0,3) at the point (1 , 1,1) .

Q2. ( , , ) = x z y z

-� xyz

Marks : 1

4x + x dx ln 4x + x c

VUSR

?� True.

?� False

Q3. Find

?�z ?�z ?�s and?�t , where z(s, t) f (r(s, t), (s, t))

Marks : 10

2r f (r, ) e sin(3 ) , r(s, t) = -�st t , (s, t)?� = s + t

Q4. Compute the volume of the solid bounded by the given surface

z = -�1 y , z = 0 , y = 0, x = 1, x = 2

Q5. Not all critical points need to be local extrema.

?� True.

?� False

Q6. Marks : 10

Marks : 1

Marks : 1

f (x, y) = 3 x -� y 2 is continuous at

?� x 2+ = y ?� x 2y ?� x 2y ?� x 2y

Q7. Find an equation of the plane through the origin that is parallel to the plane:

4x -� 2 y + 7 z +12 = 0

Marks : 5

VUSR

Q8. Use double integrals to compute the area of the region bounded by the curves:

Marks : 10

y x and y = -� x

Q9. If f ( is +ve then the graph of function is concave up.

?� True.

?� False

Q10. Direction cosines of straight line through A(1,1,1) and B(0,0,-1) are

Marks : 1

Marks : 1

-�1

?� None of these.