Math 250 Business Calculus
This is Paper Test # 4 [Go to web quiz 4]
Numerical answers are in our text, Hoffman 8th edition;
Methods will be discussed using other problems
Links to other web pages were not on original test;
CAUTION: Prof McFarland makes new tests each semester.
Mathematics 25O Test 4 (Hour Exam : perfect=45) given Spring 2009
[A] Credit given in proportion to the clarity of your WORK
[B] You need not evaluate anything beyond a point where a calulator is necessary
[C] NON-GRAPHING use of calculators is allowed |
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PRINT name above |
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grade on this test |
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credit on web quiz #4 |
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Average grade on this test : 31.17 |
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| [1](a) |
(#1 Pg 268 ; see [2] below?)(1 pt) Find f '(x)
if f(x) = -2x3 + 3x2
+12x - 5 |
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(Enter numbers in boxes) f '(x) = |
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x2 + |
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x + |
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; |
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(b)(4 pts) Find both CVs (critical values) for f(x) in [1a]
above. Then test each CV by filling all the
empty boxes of the table (right). |
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test value |
smallest
CV |
test value |
largest
CV |
test value |
| x |
-3 |
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0 |
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3 |
| f '(x) |
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0 |
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0 |
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kind of CV
Relative Max
Relative Min
or Ledge |
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 Rel. Max
Rel. Min
Ledge |
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Rel. Max
Rel. Min
Ledge |
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| [2] |
(Pg 269 #21, domain simplified; compare with [1] above)
Let f(x) =
-2x3 + 3x2
+12x - 5
with domain of f restricted to: 0 
x +1 |
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(a)(2 pts) Enter BOTH CV's of f(x) into the
2nd row of the table below. Note: domain
endpoints are CV's. |
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(b)(3 pts) Fill in the remaining empty boxes in the 3rd,
4th, and 5th rows of the table below. |
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CV |
test value |
CV |
| x |
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1
2 |
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| f (x) |
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| f '(x) |
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kind
of
CV |
Rel. Max.
Rel. Min.
Ledge |
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Rel. Max.
Rel. Min.
Ledge |
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Mathematics : The language of logic ! |
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| [3] |
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(Pg 260 part of #9) A rectangular playground will have an area of 3600 m2
(square meters) meters, and will be enclosed on all sides by a fence. |
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Write an equation expressing the relationship between the field
width "x" and
the length "P" of fence needed to enclose this playground. |
| [4] |
(a)(1 pt)(Pg 292 #1f) Use a calculator to
express e as a decimal accurate to within 0.01 |
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(b)(2 pt)(Pg 308 #27) Without using a calculator, and showing work, find x if
 x = |
1
3 |
( |
16 + 2 2 |
) |
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(c)(2 pts)(Pg 294 #45) A cookbook sold at the rates of 25,000 copies
per year on 1 January 2005, and 10,000 copies per year on 1 January 2006. If the
number of books sold is falling exponentially (i.e., Q=Qoekt with k<0), at what rate would these books be sold on
1 January 2007? (show work) |
| [5] |
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(a)(2 pts)(part of #15 Pg 214) Find y " if
y = x4 - 4x3 + 10. |
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(b)(3 pts)(more of #15 Pg 214) For the function y = x4 - 4x3 + 10 ,
find its two candidates, that is, find the two values of x for which y
" = 0, and enter these candidates in the table below |
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| [6] |
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(#15 Pg 214) Test concavity on each side of the 2 candidates in [5] above by filling in the table below. |
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| [7] |
(a)(#13,15 Pg 365)(1 pt) Find |
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( |
1
2 |
ex + |
2
x3 |
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+ |
x |
) |
dx |
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(b)(handout)(2 pts) Find |
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  dx |
(The integrand is multiplied by ) |
For the remaining 2 problems, if you use substitution, copy the left-hand
table (below) into your blue book, and fill in it's 4 empty boxes. If you use
integration by parts (IBP), copy the
right-hand table (below) into your blue book, and fill in it's 4 empty boxes.
Use no isolated differentials, i.e., do not write expressions like "du = 2xdx"
For substitution
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u = |
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y(u) = |
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For IBP
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u = |
u ' = |
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v = |
v ' = |
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[8] (#13 Pg 377) Find |
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x2 (x3 + 1)¾ dx ( ¾ is an exponent) |
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[9] (part of #5 Pg 461, done in class yesterday) Find |
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x x dx |
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dx
