Here are the answers!
1) Use rule 4 because it goes to infinity! !
2)
Use rule 2a because the num and den = 0!
3)
Use rule 3 because den = 0 but not num.!!
|
x
|
x/(x+1) |
| -1.1 |
11
|
| -1.01 |
101 |
| -1.001 |
1001 |
From the chart, you can see
that it goes to
infinity.
4) Again,
this is rule 3. But you must check on
both sides!!
| x |
|x|/x |
| .1 |
1 |
| .01 |
1 |
| .001 |
1 |
| -.1 |
-1 |
| -.01 |
-1 |
| -.001 |
-1 |
Because on one side
it approaches one and on the
other side it approaches
negative one, the limit does
not exist!!
5) Use rule 2b, because num and den = 0!!
Thus, it is 2!!
6) Use rule 2a, because num and den = 0!!
7) The only
possible point of discontinuity would
be at the point where
the function changes value.
At x = 1. Look at the graph of the function.
The point in
question is defined at (1, 1) for the
first function! Therefore, the function is
continuous!
8) Vertical asymptote at x = 3
Horizontal asymptote at y = 1
x-intercept at (0,0)
y-intercept at (0,0)
no holes!
9) Vertical asymptotes at x = 1 and x = -1
Horizontal asymptote at y = 1
x-intercept: none
y-intercept: (0,-1)
no holes!
10) Vertical asymptote at x = 0
Horizontal asymptote y = 1
x-intercept: x = -1
y-intercept: none
Hole at (-2, 1/2) Blue dot on graph!
There you have it!
Good luck on the test
and get ready for some
real calculus in
chapter 20!
