MTH301 Midterm Past Papers by Junaid

Every point in three dimensional space can be described by ------- coordinates

 Three

What are the direction cosines for the line joining the points (1, 3, 2) and (7, -2, 3)?

and

The angles which a line makes with positive x ,y and z-axis are known as ------------

Direction angles ·  Plane parallel to xz-plane · Domain of the function f (x, y, z)=

x y z is

 Entire 3D-Space

Suppose f (x, y) = xy− 2y where x2 = +3t 1 and y = 2t. Which one of the following is true?

df t t dt 

For a function f (x, y, z) , the equation ∂∂22xf +∂∂22yf +∂∂22zf =0 is known as --------

 Laplace’s Equation (Ali)

Magnitude of vector a

is 2, magnitude of vectorb is 3 and angle between them when placed tail to tail is 45 degrees. What is a b

•  4.2

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

Two surfaces are said to be orthogonal at a point of their intersection if their normals at that point are ---------

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

 In opposite direction

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

Two surfaces are said to be orthogonal at a point of their intersection if their normals at that point are ---------

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

 In opposite direction · fyy(x0, y0) − fxy2 (x0, y0) If D > 0 and fxx(x0, y0) · fyy(x0, y0) − fxy2(x0, y0) If D = 0 then --------------- ·  A unique point

Which of the following is associated to each point of three dimensional spaces?

 First

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

Two surfaces are said to be orthogonal at appoint of their intersection if their normals at that point are_________.

By Extreme Value Theorem, if a function f ( x y,) is continuous on a closed and bounded set R, then f ( x, y) has both __________ on R.

and f xy ) in some circle centered at a critical point ( x0, y0 ) and let D = fxx ( x0, y0 ) fyy ( x0, y0) − fxy 2 ( x0, y0) if D > 0 and fxx ( x0, y0 ) < 0 then f has __________ .