136.169, Assignment No. 1

September 18, 2002

The assignment is due Wednesday, September 25, 2002 in class. Late assignments receive a mark zero.

1. Let f(x) = 2-|x| and g(x) = .

a)Find the domain and the range of f and g and draw their graphs. [4]

b)Find the domains , ranges and formulas for the functions and . Draw the

graphs of and (if the corresponding function is defined).[5]

2. a) The point P lies on the x axis and the point Q lies on the line y = -2x. The point

(2,1) is the midpoint of PQ. Find the coordinates of P. [5]

b) Find the y coordinates of the points of intersection of the circle and the

ellipse . Draw a picture. [5]

3. a) Find values of sin 75^o and cos 75^o by using table 5. on page 46 and using addition

formulas on page 47. [4]

b) What is the length of the line segment having one end on the x axis, the other end

on the y axis, passing through the point ( , +1) and making an angle of

105^o with the x axis. Solve the question by using a). Draw a picture. [5]

4.Using the formal definition of the limit verify that:

a). [6]

b) If and , then . [7]

Total [ 41/40]