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.

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.

2lim 2xh 3h

h 0 h

2lim lim lim2xh 3h h (2x 3h)2x 3h

h 0 h h 0 h h 0

9.

3 x if x 410. f (x)

10 2x if x 4

Calculate the left, right and limit at 4.

11. f (x) x

Calculate the left, right and limit at 0.

lim lima. f (x) x 0x 0 x 0

lim limb. f (x) x 0x 0 x 0

limc. f (x) 0x 0

12. Use limits to describe the asymptotic behavior of this function.

f (x) 1

3 x

limf (x) 0

x

Or as x becomes very large the y value approaches 0. The x-axis, y = 0 is a horizontal asymptote.

limf (x)

x 3

Or as x approaches 3 the y value approaches . The line x = 3 is a vertical asymptote.

f (x) 2x 1x 1

13. Use limits to describe the asymptotic behavior of this function.

limf (x) 2

x

Or as x becomes very large the y value approaches 0. The line y = 2 is a horizontal asymptote.

limf (x)

x 1

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 if x 3f (x)

6 x if x 3

f (x) 7x 5

17. Determine if the function is continuous or discontinuous. If it is discontinuous, state where that occurs.

f (x) 12

5x 3 5x

18. Determine if the function is continuous or discontinuous. If it is discontinuous, state where that occurs.

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 if x 4f (x)

10 2x 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

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.

limx 0(1

x

10)1/ x

21. General: Superconductivity The conductivity of aluminum at temperature near absolute zero is approximated by the function :

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 .

f (x) 100

1 .001x 2