MTH 302 mid paper

Question No: 1 ( Marks: 1 ) - Please choose one
Which of the following is the interval notation of real line?
► (-∞ , +∞)
► (-∞ , 0)
► (0 , +∞)

Question No: 2 ( Marks: 1 ) - Please choose one
What is the general equation of parabola whose axis of symmetry is parallel to y-axis?
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Question No: 3 ( Marks: 1 ) - Please choose one
Which of the following is geometrical representation of the equation , in three dimensional space?

► A point on y-axis
► Plane parallel to xy-plane
► Plane parallel to yz-axis
► Plane parallel to xz-plane

Question No: 4 ( Marks: 1 ) - Please choose one
Suppose . Which one of the statements is correct?

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Question No: 5 ( Marks: 1 ) - Please choose one
If
then =

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Question No: 6 ( Marks: 1 ) - Please choose one
Let w = f(x, y, z) and x = g(r, s), y = h(r, s), z = t(r, s) then by chain rule


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Question No: 7 ( Marks: 1 ) - Please choose one
Is the function continuous at origin? If not, why?

► is continuous at origin
► is not defined
► is defined but does not exist
► is defined and exists but these two numbers are not equal.

Question No: 8 ( Marks: 1 ) - Please choose one
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

Question No: 9 ( Marks: 1 ) - Please choose one
Two surfaces are said to be orthogonal at a point of their intersection if their normals at that point are ---------
► Parallel
► Perpendicular
► In opposite direction

Question No: 10 ( Marks: 1 ) - Please choose one
Two surfaces are said to intersect orthogonally if their normals at every point common to them are ----------
► perpendicular
► parallel
► in opposite direction

Question No: 11 ( Marks: 1 ) - Please choose one
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.

Question No: 12 ( Marks: 1 ) - Please choose one
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.

Question No: 13 ( Marks: 1 ) - Please choose one
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
► Relative minimum at
► Saddle point at
► No conclusion can be drawn

Question No: 14 ( Marks: 1 ) - Please choose one
Let and be any two points in three dimensional space. What does the formula calculates?
► Distance between these two points
► Midpoint of the line joining these two points
► Ratio between these two points

Question No: 15 ( Marks: 1 ) - Please choose one
The function is continuous in the region --------- and discontinuous elsewhere.

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Question No: 16 ( Marks: 1 ) - Please choose one
Plane is an example of ---------------------
► Curve
► Surface
► Sphere
► Cone

Question No: 17 ( Marks: 1 ) - Please choose one
If , where and are no overlapping regions then


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Question No: 18 ( Marks: 1 ) - Please choose one


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Question No: 19 ( Marks: 1 ) - Please choose one


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Question No: 20 ( Marks: 1 ) - Please choose one


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Question No: 21 ( Marks: 2 )
Following is the graph of a function of two variables

In its whole domain, state whether the function has relative maximum value or absolute maximum value at point B. Also, justify your answer

Question No: 22 ( Marks: 2 )
Let the function is continuous in the region R, where R is bounded by graph of functions g1 and g2 (as shown below).



In the following equation, replace question mark (?) with the correct value.


Question No: 23 ( Marks: 3 )
Evaluate the following double integral.



Question No: 24 ( Marks: 3 )


Question No: 25 ( Marks: 5 )
Find, Equation of Normal line (in parametric form) to the surface at the point

Question No: 26 ( Marks: 5 )
Use double integral in rectangular co-ordinates to compute area of the region bounded by the curves , in the first quadrant.