Intro to Calculus Test 7 Mr. Holcomb 2008/2009

Name:

Problem

(8 points)

Plot the following points. Label the points with their letter
point A:

point B:

point C:

point D:

(8 points)

Write a polar equation for each of the following sets of data.
a.

2	2	2	2
	0

1	2	3	4

3	4	5	6
	0

(7 points)

a. Convert the polar coordinate

to rectangular coordinates.

b. Convert the rectangular coordinate

to polar coordinates.

.

(12 points)

Let

a. Find the slope of the line which passes through the points

and

.

b. Write an expression, in terms of

, for the slope of the line passing through

and

. Simplify your expression.

c. Suppose that you evaluated your expression from part (b) for a value of

that is really close to zero. What would your answer be really close to?

d. In calculus terms, what are you finding in part (c) of this problem?

(15 points)

The current 100 meter record for running 9.69 seconds and is held by Usain Bolt. The graph below represents this amazing run.

a. When, approxmimately, was Bolt going fastest?

b. Approximately how far did Bolt run in the first 4 seconds of the race? Justify with clear and complete calculations.

c. Estimate the derivative at 3 seconds. Justify with clear and complete calculations.

d. What does your answer to question (c) mean in terms of Bolts motion?

e. Without calculating, what’s the value of the definite integral over the interval

(11 points)

The velocity, v, as a function of time, t, of a moving object is given by

inches per minute.

a. When will the velocity equal 5 inches per minute? Show how to calculate this. Approximate to the nearest 0.1 unit.

c. Approximately how far does the object go between

and

minute? Justify with clear and complte calculations.

.

(9 points)

Lee Per attaches himself to a strong bungee cord and jumps off a bridge. At time

seconds the cord first becomes taut. From that time on, Lee’s distance, d feet, from the river is given by the equation

a. How far (to the nearest tenth of a foot) is Lee from the water when

?

b. Approximate the average rate of change of d with respect to t for the interval

and for the interval

. Round to the nearest 0.1 unit. Justify with clear and complete calculations.

c. Using your work from above, approximate Lee’s velocity at

? Is he moving up or down? Round to the nearest 0.1 unit. Justify with clear and complete calculations.