MTH301 - Calculus II

MTH301 MID FALL 2010

Suppose . Which one of the following is correct?

Let R be a closed region in two dimensional space. What does the double integral over R calculates?

Area of R.

Radius of inscribed circle in R.

Distance between two endpoints of R.

None of these

What is the distance between points (3, 2, 4) and (6, 10, -1)?

-------------------- planes intersect at right angle to form three dimensional space.

Three

4

8

12

There is one-to-one correspondence between the set of points on co-ordinate line and ------------

Set of real numbers

Set of integers

Set of natural numbers

Set of rational numbers

Let the function    has continuous second-order partial derivatives  in some circle centered at a critical point and let

If  then ---------------

 has relative maximum at

 has relative minimum at

 has saddle point at

No conclusion can be drawn.

Suppose . Which one of the following is true?

Let ,  and  be unit vectors in the direction of x-axis, y-axis and z-axis respectively. Suppose that . What is the magnitude of vector ?

6

30

A straight line is --------------- geometric figure.

One-dimensional

Two-dimensional

Three-dimensional

Dimensionless

Which of the following formula can be used to find the Volume of a parallelepiped with adjacent edges formed by the vectors ?

The function  is continuous in the region --------- and discontinuous elsewhere.

What is the relation between the direction of gradient at any point on the surface to the tangent plane at that point ?

parallel

perpendicular

opposite direction

No relation between them.

Suppose . Which one of the statements is correct?

Two surfaces are said to intersect orthogonally if their normals at every point common to them are ----------

perpendicular

parallel

in opposite direction

Let the function    has continuous second-order partial derivatives  in some circle centered at a critical point and let

If  and  then  has ---------------

Relative maximum at

Relative minimum at

Saddle point at

No conclusion can be drawn.

If  

then what is the value of ?

Q-    

2MARKS

Q -  Let the function is continuous in the region R, where R is a rectangle as shown below.

complete the following equation

2MARKS

Q.Find all critical points of the function

Evaluate 

Q-Evaluate the following double integral.

3MARKS

Q-  Let . If  changes from 3 to 3.3, find the approximate change in the value of y using differential dy.

3MARKS