The King’s University College

Math 300 - Midterm Exam I

Monday, October 23, 2006

 

 

Please answer the following questions as completely as you can, in the booklet provided.  The value of each question is indicated.

 

1.      Short Answer questions - 2 marks each

a.           Vector a passes through points (1,3,1) and (-2,3,4). Is the vector n = <1,4,1> parallel, perpendicular or skew to vector a?

b.           Sketch  a polar graph of r = q.  What shape is this?

c.           Find  for the relation given parametrically by .

d.           Use the power series expansion for sin(x)  () and your knowledge about sine and cosine to derive a series expansion for cos(x).

e.           Prove or disprove that the point (4,1,-2) lies in the plane given by the linear form

 

 

2.      Sketch the graphs for  and  and find where they intersect (5 marks). Determine the area formed by the intersection of these graphs? (5 marks). (Hint: recall that in polar form )

3.      Use power series techniques to evaluate the integral  (5 marks)

4.      Answer the following about the planes  and :

a.           What are the normal vectors for the two planes? (2 marks)

b.           What is the angle formed by the intersection of the planes? (3 marks)

c.           What is the equation of the line formed by the intersection of the planes? (5 marks)

 

 

 

The End