This is Paper Test # 6 [Go to web quiz 6]

Numerical answers are in our text, Hoffman 11th 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.

 Math 250 Test 6 Spring 2017
 Average grade on this test : 32.31
 Perfect score = 45

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paper test   web quiz
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Total (max = 45)
 I lovesummervacation !
 [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

[1] (a)(#37 Pg 420, 3 numbers changed, method same)(3 pts) Find ( 2x - 4 )6   dx

hint
u =
 dudx =
y(u) =
 dydu =
(b)(#37 Pg 420 cont'd)(2 pts) Show that
 2 1
( 2x - 4 )6   dx   =     64
7
[2] (a)(part of #21 Pg 451)(3 pts) On the figure at the right are the graphs of
[ y = 7250 - 18x2 ] and [ y = 3620 + 12x2 ].
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.

( x2 + x + ) dx
(b)(more of #21 Pg 451; you may use a calculator ONLY to add and multiply)(2 pts, for work only) Evaluate the integral in [2](a) above, and thus discover that the area shaded in the figure above is exactly 26620.
[3]
 (a)(Pg 438 #35, simplified)(3 pts) WP&L supplies S(x) = ( 0.9x2 + 6 ) megawatts of power at time x ; what was the average number of megawatts supplied from time x=2 to x=5? Answer is between 10 and 18.
 (b)(#17 Pg 786, one number changed)(2 pts) For the geometric series n=0 3  (-4)n , write (for 1 pt) its first 4 terms, and (for 1 more pt) the sum of all its infinitely many terms.
[4]
 (a)(3 pts)(#3 Pg 704) Write the GENERAL SOLUTION of the differential equation y' = 3y
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 ].

(b)(2 pts)(more of #3, 21 Pg 704) Find the PARTICULAR solution of [ y' = 3y ] for which
 y = 1 e when x = 2
[5] (a)(#7 Pg 515, one number changed)(3 pts) Find
 3
(x - 1)- 2   dx   (Show limit process)
 (b)(#35 Pg 786)(2 pts) Write the repeating decimal 0.252525.... as a reduced fraction of integers, like 1341
 [6] (#3 Pg 584, voted in) Use least squares method to find the line best fitting the data points : (1,2) , (2,4) , (4,4), and (5,2)
[7] (a)(Pg 572 #9, 2 numbers changed)(2 pts) Find fx , fy , fxx , fxy , and fyy where f(x,y) = x3 - 4xy + y3 .
(b)(more of Pg 572 #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.
(c)(rest of Pg 572 #9)(2 pts) Complete the table below using your results in (7a) and (7b) above:
CP A = fxx B = fxy C = fyy D = AC - B2 Kind of CP:
Relative Maximum,
Relative Minimum,
(0,0)
 ( 4 3 , 4 3 )

[8](a)(part of Pg 618 #11)(3 pts) Evaluate (showing work)
 0
x2y dy
 The answer to [8a] is ½x3 The answer to [8b] is 32
(b)(Rest of Pg 618 #11)(2 pts) Evaluate the double integral:
 4 0
 0
x2y dy dx
The algebra and calculus are fairly easy. Credit only for work. Note [C] at top of test.

[9]
 (a)(Pg 811 #15)(3 pts)Fill in the table at the right for the function f(x) = e - x (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) = e - x
 n function: f (n)(x) value at    x = 0 an 0 1 2 3