Math 76O-250 Business Calculus
This is Paper Test # 6 [Go to web quiz 6]
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.
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Math 250 Test 6 Spring 2009 |
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Average grade on this test : 33.00 |
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__________________
PRINT name above |
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I love
summer
vacation ! |
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[A] Except perhaps for problems [2], [7], [9], put answers/work in blue book
[B] Credit given in proportion to the clarity of your WORK
[C] Use no isolated differentials. E.g., do not write "dy = 3xdx"
[D] You need not evaluate anything beyond a point where a calulator is needed
[E] NON-GRAPHING use of calculators is permitted |
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(a)(#13 Pg 396, 3 numbers changed, method same)(3 pts) Find |
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(4x3 + x) |
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dx |
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(b)(#13 Pg 396 cont'd)(2 pts) Show that |
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(4x3 + x) |
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dx = |
7
3 |
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(part of #11 Pg 410)(5 pts) On the figure at the right are the
graphs of
[ y = x2 - 2x ] and [ y = -x2 + 4 ]. |
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Without using a graphing calculator, express the area shaded at the right as a single definite
integral by entering specific integers (such as 3, -2, or 0) in the 5 empty
answer boxes below. Show some algebraic work, especially in finding the two limit
numbers immediately to the right of the integral sign, but you need not find the value of above integral.
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x2 +
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x +
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dx |
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(a)(Pg 410 #35)(3 pts) The price of ground beef x months
after 1 January 2005 at Sentry Food Store was
P = 0.09x2 - 0.2x + 1.6 ;
what was the average price of ground beef during the first 3 months of
2005 (through the end of March)? |
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(b)(#17 Pg 670, one number changed)(2 pts) For the geometric series |
n=0 |
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3
(-4)n |
, write |
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(for 1 pt) its first 4 terms, and (for 1 more pt)
the sum of all its infinitely many terms. |
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(a)(3 pts)(#3 Pg 599) Write the GENERAL SOLUTION of the differential
equation y' = 3y |
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Your answer will be an equation with no "x" on the left side,
and no "y" on the right side.
Your answer should not contain y'. For example, the
GENERAL SOLUTION of [ y' = 2x ] is [ y = x2 + C ]. |
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(b)(2 pts)(part of #13 Pg 517) If z = x ln y,
write the partial derivatives zx and zy |
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| [5] |
(a)(#7 Pg 470, one number changed)(3 pts) Find |
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(x - 1)- 2 |
dx |
(Show limit process) |
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(b)(#27 Pg 670)(2 pts) Write the repeating decimal 0.252525....
as a reduced fraction of integers, like |
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41 |
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(#3 Pg 540, voted in) Use least squares method to find the line best
fitting the data points :
(1,2) , (2,4) , (4,4), and (5,2) |
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(a)(Pg 528 #9, 2 numbers changed)(2 pts) Find fx , fy , fxx ,
fxy , and fyy where
f(x,y) = x3 + y2 - 6xy + 12x + 4y + 2 . |
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(b)(more of Pg 528 #9)(1 pt) Show algebra work used to find the critical
points (CP's) for the function f(x,y) in (7a) above. The CP's are given in the
table below. |
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(c)(rest of Pg 528 #9)(2 pts) Complete the table below
using your results in (7a) and (7b) above: |
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A = fxx |
B = fxy |
C = fyy |
D = AC - B2 |
Kind of CP:
Relative Maximum,
Relative Minimum,
or Saddle Point? |
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| (2,4) |
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[8](a)(part of Pg 570 #11)(3 pts) Evaluate (showing work) |
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x2y dy |
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The answer to [8a] is ½x3
The answer to [8b] is 32 |
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(b)(Rest of Pg 570 #11)(2 pts) Evaluate the double integral:
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x2y dy dx |
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The algebra and calculus are fairly easy. Credit only for work.
Note [C] at top of test. |
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(a)(Pg 697 #15)(3 pts)Fill in the table
at the right for the function
f(x) = e3x |
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(b)(2 pts) Use your table entries
(at the right) to write the
first four terms of the
Taylor series about (a=0) for the
function f(x) = e3x |
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function: f (n)(x) |
value at
x = 0 |
an
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| 1 |
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| 2 |
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| 3 |
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2x4 + x2 + 1