Time and Date Stamps (logged): 01:32:02 08-29-2008
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Precalculus II
Calculus I Test 2
Completely document your work and your reasoning.
You will be graded on your documentation, your reasoning, and the
correctness of your conclusions.
Test should be printed using Internet Explorer. If
printed from different browser check to be sure test items have not been cut off. If
items are cut off then print in Landscape Mode (choose File, Print, click on Properties
and check the box next to Landscape, etc.).
- Write on ONE SIDE of paper only
- If a distance student be sure to email
instructor after taking the test in order to request results.
Name and Signature of Student
_____________________________
Signed by Attendant, with Current Date and Time:
______________________
If picture ID has been matched with student and name as
given above, Attendant please sign here: _________
Instructions:
- Test is to be taken without reference to text or
outside notes.
- Graphing Calculator is allowed, as is blank paper or
testing center paper.
- No time limit but test is to be taken in one
sitting.
- Please place completed test in Dave Smith's folder,
OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va.,
24212-0828 OR email copy of document to dsmith@vhcc.edu,
OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken. Student may, if proctor deems it feasible, make and retain a copy of the test..
Directions for Student:
- Completely document your work.
- Numerical answers should be correct to 3 significant
figures. You may round off given numerical information to a precision consistent
with this standard.
- Undocumented and unjustified answers may be counted
wrong, and in the case of two-choice or limited-choice answers (e.g., true-false or
yes-no) will be counted wrong. Undocumented and unjustified answers, if wrong, never get
partial credit. So show your work and explain your reasoning.
- Due to a scanner malfunction and other errors some
test items may be hard to read, incomplete or even illegible. If this is judged by
the instructor to be the case you will not be penalized for these items, but if you
complete them and if they help your grade they will be counted. Therefore it is to
your advantage to attempt to complete them, if necessary sensibly filling in any
questionable parts.
- Please write on one side of paper only, and staple
test pages together.
Test Problems:
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Problem Number 1
Find the derivative of y = -7 cos (-9 `pi e^( 6 x) ) ).
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Problem Number 2
If the function y = .018 t2 + -1.7 t + 88 represents depth y vs. clock time t,
then what is the average rate of depth change between clock times t = 12.8 and t = 25.6?
- What is the rate of depth change at the clock time halfway between t = 12.8 and t = 25.6?
What function represents the rate r of depth change at clock time t?
- What is the value of this function at the clock time halfway between t = 12.8 and t =
25.6?
If the rate of depth change is given by dy/dt = .057 t + -2.5 represents the rate at which
depth is changing at clock time t, then how much depth change will there be between clock
times t = 12.8 and t = 25.6?
- Give the function that represents
the depth. What would this specific function be if at clock time t = 0 the depth is 180?
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Problem Number 3
At clock time t the position of a certain mass oscillating at the end of a
certain spring is y(t) = 6 sin ( .5 `pi t ) + 7.
- Find the corresponding functions for the velocity v(t) and acceleration a(t) of
the spring at clock time t.
- Determine the first clock time t when the position is greatest and when it is
zero.
- Determine the first clock time t when the velocity is greatest and when it is
zero.
- Determine the first clock time t when the acceleration is greatest and when it is
zero.
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Problem Number 4
Problem: At what average rate does the exponential intensity function
I(t) = 93 * .91 ^ t change between clock times 3.3 and 3.31?
- Write the same expression for the intensity function I(t) = I0 * b ^ t.
- Using the laws of exponents simplify your expression as much as possible.
Problem: If a sandpile 2 meters in diameter contains $ 78 worth
of sand, then what function gives the value of geometrically similar sandpiles as a
function of diameter in meters?
- How much would it cost to increase the diameter of this sandpile to
2.01 meters?
- What average rate is the cost of the sandpile increasing with respect to
diameter between these two diameters?
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Problem Number 5
Sketch a smoothly curving continuous graph with three points A, B and C, each to the
right of the preceding, such that the following quantities occur in the given order, from
least to greatest:
The slope at C
The average slope between B and C
The slope at B
The slope at A
The average slope between A and B.
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Problem Number 6
y = sin^2 x - .5 cos x is defined on the closed interval [0, 2]. Find all
relative maximia and minima, and find the global maximum and the global minimum on this
interval.
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Problem Number 7
Using the first-derivative test determine the coordinates of the extreme point
of the function y = 1.599 cos (-3.2 - -6.44 x), and determine whether this point is a maximum or a
minimum.
Use a second-derivative test to confirm whether this point is a maximum or a
minimum.
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Problem Number 8
Without computing an integral show that the average value of cos( 6 x) on the interval
(0, `pi / ( 12) ) is greater than .5.