Section 1.4
2.
use window [0,2] by [0,5]
Note you cannot plug 1 into this equation. However, your calculator will help
you. Do you see the “hole” at (1, 1)? Go to table set, start at 0.9 and tbl = .05
and you will see the limit of 1 under table.
3.
Plug the 3 into the function.
4.
Plug the 5 into the function.
5.
6.
Plug the 0 into the function for h.
7.
Plug the - 3 into the function.
8.
lim 2xh  3h 2
h0
h
You need to get rid of the h in the bottom. Factor the h out of the top and
cancel it with the h in the bottom. Then plug the 0 into the function for h.
lim 2xh  3h2
lim h (2x  3h)
lim


2x  3h
h0
h
h0
h
h0
9.
3  x
10. f (x) 
10  2x
if x  4 

if x  4 
Calculate the left, right and limit at 4.
11.
f (x)  x
Calculate the left, right and limit at 0.
lim
lim
a.
f (x) 
x0


x0
x0
lim
lim
b.
f (x) 
x0


x0
x0
lim
c.
f (x)  0

x0
12. Use limits to describe the asymptotic behavior of this function.
1
f (x) 
3 x

lim
f (x)  0
x
lim
f (x)  
x3
Or as x becomes very large the y value
approaches 0. The x-axis, y = 0 is a horizontal
asymptote.
Or as x approaches 3 the y value approaches .
The line x = 3 is a vertical asymptote.
13. Use limits to describe the asymptotic behavior of this function.
2x 1
f (x) 
x 1
lim
f (x)  2
x
lim
f (x)  
x1
Or as x becomes very large the y value
approaches 0. The line y = 2 is a horizontal
asymptote.
Or as x approaches 3 the y value approaches .
The line x = 1 is a vertical asymptote.
14. Determine if the following function is continuous or discontinuous. If it is not
state why it is not.
It is continuous.
15. Determine if the following function is continuous or discontinuous. If it is not
state why it is not.
c
16 . a. Draw the graph of the following function.
b. Find the limits as x approaches 3 from the left and the right.
c. Is it continuous at 3? If not state why.
x
f (x)  
6  x
if x  3
if x  3

17. Determine if the function is continuous or discontinuous. If it is discontinuous,
state where that occurs.
f (x)  7x  5
18. Determine if the function is continuous or discontinuous. If it is
discontinuous, state where that occurs.
12
f (x)  3
5x  5x

OR use your calculator and table to examine what occurs at x = 0, -1 and 1.
19. Determine if the function is continuous or discontinuous. If it is discontinuous,
state where that occurs.
3  x
f (x) 
10  2x
if x  4 

if x  4 
From problem 10 we know that there is no limit. Therefore, the function is
not continuous.
20. Business: Interest Compounded Continuously If you deposit $1 into
a bank account paying 10% interest compounded continuously, a year later
its value will be
x 1/ x
lim (1 )
x0
10
Find the limit by making a TABLE of values correct to two decimal places, thereby
finding the value of the deposit in dollars and cents.

21. General: Superconductivity The conductivity of aluminum at temperature
near absolute zero is approximated by the function :
100
f (x) 
1 .001x 2
which expresses the conductivity as a percent.
Find the limit of this conductivity percent as the temperature
x approaches 0 (absolute zero) from the right .