Time and Date Stamps (logged): 23:22:04 10-15-2008
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Calculus II
Calculus II Test 1
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- 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:
______________________
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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 general solution of dy / dt = 3 cos( 9 t) - .3.
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Problem Number 2
Integrate x arctan(x^2) with respect to x, from x = 1.6 to x = 2.4.
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Problem Number 3
Determine whether the antiderivatives of e^( 3 x) / (1 + e^ 3 x) and cos( 3 x) /
(1 + cos( 3 x)) are in fact different expressions of the same problem. If so specify
the problem; if not state why not.
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Problem Number 4
If water is entering a sphere at 21 cm^3 / second, then at what rate in cm/sec
is water rising in a sphere of radius 41 cm when water depth is 40 cm?
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Problem Number 5
Find the integral of sin(`sqrt(x) ) / [ 4 `sqrt(x) ], between x = 1.5 and
x = 2.5, in two ways.
- First find an antiderivative of the function, in terms of the original variable
x, and apply the First Fundamental Theorem.
- Then use an appropriate u = ... substitution and rewrite the integral in terms of
u. Don't convert the antiderivative back to the original variable, but simply apply
the First Fundamental Theorem to an antiderivative expressed in terms of u.
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Problem Number 6
Sketch a graph of a smooth curve which is asymptotic to y = 3 for negative
values of x and to y = - 3 for positive values of x, and which passes through the origin.
Assuming that this graph represents the function f '', sketch graphs of f ' and f,
assuming that both graphs pass through the origin.
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Problem Number 7
Find the general antiderivative of t sin( 5 t^2).
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Problem Number 8
Find the area between the graphs of y = z^2 / 3 + 7 and y = 7 z.