©Zarestky
Math 142 Quiz 1 Version B
1/27/2011
NAME:________KEY________________________________
1.
(3 pts) Solve for x: x 2 e x !3xe x = 0
Factor: x 2 e x !3xe x = e x ( x 2 !3x ) = e x ( x )( x !3) = 0
Then e x = 0 or x = 0 or x !3 = 0 . Note that e x never equals 0.
The solutions to the equation are x = 0,3 .
2.
(4 pts) Use the graph of y = f ( x ) , below right. (You may assume the y-axis has the same scale as the
x-axis.)
lim f ( x ) = 4
x!2
lim f ( x ) = 2
x!1
3.
(3 pts)
lim
x!4
( x + 4)( x " 4)
x 2 "16
= lim ( x + 4) = 8
= lim
x!4
x!4
x"4
x"4
Bonus (2 pts): What is a rational function? (This is from the 3.2 reading notes but you may not use your notes.
Your answer doesn’t have to be technical; a sentence will suffice.)
A rational function is a function consisting of one polynomial divided by another polynomial.