Time and Date Stamps (logged): 17:12:20 06-10-2020
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Precalculus II
Calculus I Test 1
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
Sketch the graph of f(x) = 1 / (x + 6), from x = -4 to x = 5, then use this
graph to sketch the graph of the derivative function f ' (x) over the same interval.
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Problem Number 2
The cost in dollars of producing n steel bars is C(n).
- What are the units of C’(n)?
- What would it mean for C’( 4300) to equal 6149?
- What could you conclude if you knew that C’( 5000) = 10670 and C( 5000) = 5500, and what would
be the practical meaning of your conclusion?
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Problem Number 3
Explain in terms of rates and amounts why and how, given the values of a derivative
function y ' (t) at two nearby t values, we can estimate the change in its antiderivative
y(t) between these t values by averaging two values of y ' (t) and multiplying by the
corresponding time interval.
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Problem Number 4
The rate at which dollars flow into your bank account is rate = 4 * 2^( .12 t),
where rate is in dollars per day when t is time in months from an initial investment.
Use two 2-interval approximations to estimate the change in the value of your
account between t = 9 months and t = 15 months. One of your approximations should
be an overestimate, the other an underestimate.
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Problem Number 5
In terms of two simple examples involving money, pay rate and time, explain the
difference between a situation where you obtain a meaningful result by subtracting two
quantities and dividing by a time interval and a situation where you obtain a meaningful
result by averaging two quantities and multiplying by a time interval. Be sure to explain
your results in terms of units and also in terms of meanings.
In terms of two simple examples involving velocity, distance and time, explain the
difference between the meaning of the slope of a trapezoid and the area of a trapezoid. Be
sure to explain your results in terms of units and also in terms of meanings.
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Problem Number 6
Solve using ratios instead of functional
proportionalities:
- If an ice cream cone 2.2 inches high contains 26.62
cal, then how many cal would we expect a geometrically similar ice cream cone 6.1 inches
high to contain?
- If ice cream initially melts from the surface of
the first cone at a rate of 23.2804 grams per minute, then and what rate will ice cream melt
from the surface of the second cone under the same conditions?
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Problem Number 7
Problem: The quadratic depth vs. clock time model corresponding to depths of 24.06623 cm,
10.40932 cm and 3.029289 cm at clock times t = 10.98677, 21.97353 and 32.9603 seconds is depth(t) = .026 t2
+ -2.1 t + 44.
- Show the system of equations we would solve to get this model.
Then use the model to determine the clock time at which depth is 8 cm.
Problem: The depth function depth(t) = .026 t2 + -2.1 t + 44 corresponds to
depths of 24.06623 cm, 10.40932 cm and 3.029289 cm at clock times t = 10.98677, 21.97353 and 32.9603 seconds.
- What system of equations would we solve to get this model?
According to the model, at what precise clock time will the rate of depth change be
- .0234 cm / sec?