Rates of Change Unit 1 Test
14
K/U
14
Comm
11
Think
18
App
Name ________________________________
Knowledge/Understanding (14 marks)
Identify the choice that best completes the statement or answers the question. Put all multiple choice answers in the box
on page 4
1. Evaluate the limit, if it exists:
.
a. does not exist
b. 2
c. 0
d. 1
2. Evaluate the limit, if it exists:
.
c. –1
d. 1
a. 0
b. does not exist
3. Evaluate the limit:
.
c. –1
d.
a. 0
b. 1
4. Evaluate the limit:
.
a. 25
b. 2.5
5. Evaluate the limit:
c.
d.
.
a.
b. –2
c. 0
d.
6. The average rate of change of
a.
b. 2a
over the interval
c.
d. 1
7. The difference quotient finds the
a. instantaneous rate of change
b. jump discontinuity
c. average rate of change
d. infinite discontinuity
is
8. Evaluate the limit for the graph:
.
a.
b. 0
9. Evaluate the limit for the graph:
c. 1
d.
.
a. 0
b. –1
10. Evaluate the limit for the graph:
a. 3
b. –1
c. 2
d. does not exist
.
c. 0
d. does not exist
11. Evaluate the limit for the graph:
a. 1
b. 3
.
c. 0
d. does not exist
12. This function:
a. has a jump discontinuity
b. has an infinite discontinuity
c. has a removable discontinuity
d. is continuous
13. This function:
a. has a jump discontinuity
b. has an infinite discontinuity
c. has a removable discontinuity
d. is continuous
14. The domain of the function is
a.
b.
c.
d.
Please put all your answers for the multiple choice questions in the respective box
below:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12
13.
14.
Communication (14 marks)
Complete each statement.
15. A one-sided limit can be used to determine the behaviour of a graph on either side of a _______________.
16. A graph is _______________ if the left-hand limit does not equal the right-hand limit as
.
17. The average rate of change is found using the _______________.
18. The instantaneous rate of change is found using _______________.
19. The limit of a function at x = a may exist even though the function is _______________ at x = a.
20. When direct substitution of x = a into a limit results in
, the limit is said to be of an _______________ form.
21. If the derivative does not exist at a point on the curve, the function is _______________ at that x-value.
22. If a function is discontinuous, or has a cusp or a corner at x = a, then the function is _______________ at x =
a.
23. Consider the following graph of f(x). Is the graph continuous? If not, where is it discontinuous and explain
the type of discontinuity. (3 marks)
24. Distinguish between average and instantaneous rate of change, use an appropriate example to support your
answer. (3 marks)
Thinking (11 marks)
25. Determine the average rate of change of
over the interval
. (3 marks)
26. Determine the average rate of change of the function over the domain graphed. (2 marks)
27. Determine the average rate of change of the function over the domain graphed. (2 marks)
28. Given
marks)
, use the difference quotient to find the instantaneous rate of change when x = 2. (4
Application (18 marks)
29. The surface area of an inflating weather balloon is described by
where x is the number of
seconds where A is measured in L.
a) Determine the average rate of change between 2 sec and 8 sec. (3 marks)
b) Determine the instantaneous rate of change at 6 seconds using the difference quotient. (3 marks)
30. Evaluate each limit, it it exists. Show all steps. (12 marks)
a)
b)
c)
d)
e)
f)