Calculus I                                                                 Diagnostic Quiz                                             September 3, 2002

Name____________________                                 R.  Hammack                                                   Score ______

Find all solutions:
  (x + 2)(x - 3) = 0
  Solutions x = -2 and x = 3.

Find all solutions:    [Graphics:Images/quiz1_gr_3.gif]
It doesn't factor, so we use the quadratic formula.
Solutions are [Graphics:Images/quiz1_gr_4.gif][Graphics:Images/quiz1_gr_5.gif][Graphics:Images/quiz1_gr_6.gif][Graphics:Images/quiz1_gr_7.gif][Graphics:Images/quiz1_gr_8.gif]

(c) Find all solutions:    [Graphics:Images/quiz1_gr_9.gif]
For this equation to be true, either x=0 or cos(x)=0.
The values of x that make cos(x) equal to 0 are [Graphics:Images/quiz1_gr_10.gif], where k is an integer.
Thus, this equation has infinitely many solutions:
x = 0, and [Graphics:Images/quiz1_gr_11.gif], where k is an integer.

(d) Find all solutions:   
Solutions x=0 and x=3


Sketch the graph of   [Graphics:Images/quiz1_gr_18.gif]
To find the x intercept, set y=0 and solve for x. You get x=6.
To find the y intercept, set x=0 and solve for y. You get y=-3.