Calculus.docx

1. The monthly cost of driving a car depends on the number of miles driven. Juan found that in May it cost him $380 to drive 480 miles and in June it cost him $460 to drive 800 miles.

a) Express the monthly cost as a function of the distance driven , assuming that a linear relationship gives a suitable model.
b) Use part a) to predict the cost of driving 1500 miles per month.
c) Draw the graph of the linear function. What does the slope represent?
d) What does the intercept represent?
e) Why does a linear function give a suitable model in this situation?
2. Use the table to evaluate each expression.

1

2

3

4

5

6

3

1

4

2

2

5

6

3

2

1

2

3

a)
b)
c)
d)
e)
f)

3. For the function whose graph is given, Find the limit or value, or explain why it does not exist.

a)
b)
c)
d)
e)
f)
g)
h)
4. Evaluate the limit using the limit laws or create a table to find the limit – you do not need to state the laws.

a.

b.

[15 points]
5.
Let

Find the following:

a.

b.

c.
Does exist?

[
6. Consider the piecewise-defined function:

a) Find

b) Determine the domain of

c) Locate any intercepts

d) Sketch the graph of the function

e) Use the graph to find the range of

f) Determine the intervals for which the function is continuous.

7. Knowing that: , what values of guarantee that is within

a) 1 unit of 3?

b) 0.6 units of 3?

c) 0.09 units of 3?

d) units of 3?
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