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