Time and Date Stamps (logged): 17:12:20 06-10-2020
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Calculus I
Calculus I Major Quiz
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
Problem: Derive the expression for the derivative of the function y(t) =
a t3 at clock time t.
Problem: If the rate of depth change is rate(t) = .036 t + -1.7, then what
is the depth function if the depth at clock time t = 0 is 78? How long does it take for
the depth to decrease from 45.51527 to 38.82575? What is the average rate which depth changes over
this period?
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Problem Number 2
Problem: Write the differential equation expressing the statement that the rate which
the temperature T changes with respect to time t is proportional to the difference between
the temperature T and the 15 degree room temperature.
Problem: If dy / dt = .98 y^2 + 1.04 y/(t+1), and if at t = 0 we have y = 1.25, then find
the approximate value of y when t = .4. Using the new values of y and t, find
approximate value y when t = .8. Continue for two more steps to find the approximate
value of y when t = 1.6.
(extra credit): Use a predictor-corrector method, with `
Dt = .8 instead of the .4 used above, to find the
approximate value of y when t = 1.6. Which value do you think is more accurate?
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Problem Number 3
If the function y = .023 t2 + -1.9 t + 86 represents depth y vs. clock time t,
then what is the average rate of depth change between clock times t = 10.9 and t = 21.8?
- What is the rate of depth change at the clock time halfway between t = 10.9 and t = 21.8?
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 = 10.9 and t =
21.8?
If the rate of depth change is given by dy/dt = .049 t + -2.7 represents the rate at which
depth is changing at clock time t, then how much depth change will there be between clock
times t = 10.9 and t = 21.8?
- Give the function that represents
the depth. What would this specific function be if at clock time t = 0 the depth is 200?
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Problem Number 4
Determine the average rate of change of the function y(t) = .1666667 t 4 between
t and t + Dt.
What are the growth rate, growth factor and population function P(t) for an initial
population of 1070 which has an annual growth rate of 10%?
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Problem Number 5
Sketch and completely label a trapezoidal approximation graph for the function y =1 +
(x+1) -3, for x = 0 to 2.4 by increments of .8.