Time and Date Stamps (logged): 01:42:03 08-29-2008
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Applied Calculus I
Applied Calculus I Major Quiz
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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 instantaneous rate of change of the function
y(t) = a t^2 + b t + c at clock time t.
Problem: If the rate of depth change is rate(t) = .028 t + -1.1, then what is the depth
function if the depth at clock time t = 0 is 54? At what instant does the flow cease, and
what is the depth at that instant?
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Problem Number 2
Problem: Write the differential equation expressing the statement that the rate which
the depth y of water changes with respect to time t his proportional to the square root of
the depth.
Problem: If dy / dt = 1.12 y + 1.13 / (t+1), and if at t = 0 we have y = .55, 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 .5 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 = .029 t2 + -1.4 t + 88 represents depth y vs. clock time t,
then what is the average rate of depth change between clock time t = 6.4 and clock time t
= 12.8? What is the rate of depth change at the clock time halfway between t = 6.4 and t =
12.8?
What function represents the rate r of depth change at clock time t? What is the clock
time halfway between t = 6.4 and t = 12.8, and what is the rate of depth change at this
instant?
If the function r(t) = .211 t + -1.8 represents the rate at which depth is changing at
clock time t, then how much depth change will there be between clock times t = 6.4 and t =
12.8?
- What function represents the
depth?
- What would this function be if it
was known that at clock time t = 0 the depth is 80 ?
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Problem Number 4
The Celsius temperature of a hot potato placed in a room is given by the function T =
67* 2- .0096 t + 23 , where t is clock time in seconds and T is
temperature in Celsius.
- At what average rate is the temperature of the potato changing between clock times t =
14.6 and t = 14.7 seconds seconds?
- At what average rate is the temperature of the potato changing between clock times t =
14.6 and t = 14.61 seconds?
- At what average rate is the temperature of the potato changing between clock times t =
14.6 and t = 14.601 seconds?
- What do you estimate is the rate at which temperature is changing at clock time t = 14.6
seconds?
The rate at which the Celsius temperature of a hot potato placed in a room is given by
Rate = .04 * 2- .0096 t, where R is rate of change in Celsius degrees per second
and t is clock time in seconds. How much temperature change do you estimate would
occur between t = 14.6 and t = 29.2 seconds?
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Problem Number 5
Sketch and completely label a trapezoidal approximation graph for the function y = 2
x/ 6, for x = 0 to 2.7 by increments of .9.
