Weekly Tutorial 6 for Math. 69.007A,
Introductory Calculus I

Instructor: Dr. Angelo Mingarelli

Notes: These are group tutorials; each question is to be divided among the group (at most 5 students in a given group), solved and submitted to the T.A. at the end of the 50 min. period. NOTES PERMITTED, along with group interaction...All students within a group will be assigned the same grade for this tutorial...
This online test is meant to be printed and handed in.
Solutions will appear later on during the term ...

Group names (Please PRINT) & Student Numbers:

1. Find the horizontal asymptotes of y = x / {|x| + 2}.
a) y = 1 and y = 1/2
b) y = 1 only
c) y = 1 and y = -1
d) y = 1/2 only
e) None of these

2. Evaluate lim x -> - inf { 4x / sqrt(x2 + 8) }.
a) 1
b) -1
c) 0
d) This limit does not exist
e) None of these

3. What are the horizontal and vertical asymptotes of the curve described by y = x2 / (x+2)2.
a) y = 0 and x = -1
b) y = -1 and x = -2
c) y = 1 and x = -2
d) None of these

4. What are the horizontal and vertical asymptotes of the curve described by y = sqrt(x2 + 5x +1) - x.
Hint: Rationalize this expression.

a) y = 1
b) y = -5/2 is the only finite asymptote
c) y = 5
d) y = 5/2 is the only finite asymptote
e) None of these

5. What are the horizontal and vertical asymptotes of the curve described by y = 2x2/ (x2 + 3x - 4).
a) y = 2 and x = -4 and x = 1
b) y = 2 and y = -2, x = -4 and x = 1
c) y = -2 and x = 1
d) y = 2 and x = -4
e) None of these

Solutions are given within the box: