MTH301 Midterm Objective

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

3. Calculator is allowed.

Q1. Marks : 5

f x y z x z y z xyz (1, 1,1) u D f G Find the directional derivative of in the

direction of at the point (1 ( 1,0,3) u = − G 1,1)

Q2. Marks : 1

ln 4 dx x x c x x  True.

 False

Q3. Marks : 10

Find

z z and s t , where z(s,t) f (r(s, t), (s,t)) θ

2r f (r, ) e sin(3 ) , r(s,t) st t (s,t) s t θ θ θ

Q4. Marks : 10

Compute the volume of the solid bounded by the given surface 0 , 0, 1, z y z y x x

Q5. Marks : 1

Not all critical points need to be local extrema.

 True.

 False

Q6. Marks : 1

f (x, y) x y

x y x y ≥ 3 x y ≤ 3 x y < 3

Q7. Marks : 5

Find an equation of the plane through the origin that is parallel to the plane: x y z

Q8. Marks : 10

Use double integrals to compute the area of the region bounded by the curves: y x and y x

Q9. Marks : 1

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

 True.

 False

Q10. Marks : 1

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

 None of these.