ACOW LIMITS AND CONTINUITY MODULE
Updated 5/28/2016
Page 1 of 2
Activity A2 – Finding Infinite Limits Graphically
Many functions we work with in calculus contain vertical asymptotes like the graph(RS1)
shown at right. To investigate the limit as x → 2 of the function graphed at right, use the
limit applet(RS2) and fill in the appropriate cells to find
x 1
lim
, 3  x  8 .
x2 x  2
Click on Value to find the value of the function and Limit to find the limit of the
function. The display in the blank portion at the bottom of the applet should look like the
following:
Notice since lim f ( x)   and lim f ( x)   , the lim f ( x)  DNE .
x 2
x2
x2
1. Use the limit applet to find the following limits given
x2
, 3  x  1.
f ( x) 
x2
(Enter INF for positive infinity and –INF for negative infinity.)
a) f (2)
b) lim f ( x)
x 2
c) lim f ( x)
x 2
d) lim f ( x)
x 2
2. Use the limit applet to find the following limits given
1
f ( x)  2 , 1  x  1
x
(Enter INF for positive infinity and –INF for negative infinity.)
a) f (0)
b) lim f ( x)
x 0
c) lim f ( x)
x 0
d) lim f ( x )
x 0
ACOW LIMITS AND CONTINUITY MODULE
Updated 5/28/2016
Page 2 of 2
3. Use the limit applet to find the following limits given
 x 2  2 2  x  0

f ( x)   x  2
0 x2

 x 1
(Enter INF for positive infinity and –INF for negative infinity.)
a) f (0)
e) f (1)
b) lim f ( x)
f) lim f ( x)
x 0
x 1
c) lim f ( x)
g) lim f ( x)
d) lim f ( x )
h) lim f ( x )
x 0
x 0
x 1
x 1