The above information is from your computer : be sure it is correct. For grade credit, submit over the internet by 11:59 PM (= 23:59 hours) on Sunday 9 December 2018 
Average grade on Fall 2017 paper test #6 : 31.51  perfect = 45  See future grade prospects? 


[2]  (a)(1 pt) On the graph at the right, click those boxes located in the region R bounded by the curve y = x^{3}  x (red) and the curve y = 2  2x^{2} (green). On paper tests, you must shade these areas 


(b)(3 pts) Enter integers below (such as 4, 0, or 3) to express the
size of the region R (in question [2a] above) as one definite integral: It is possible to use 2 integrals, but here, use only one Scoring: Limits (just after the integral sign) worth 1 point, integrand (in parenthses) worth 2 points 



(c)(1 pt) Find the size of the region you drew in [2a] above by
evaluating the integral which you wrote as an answer in (2b) above. (size of R) = 
[3]  (a)(3 pts) If the value (in $ billions) of "dotcom" stocks on the NASDAQ is V(t) = 4 + e^{x}, where x is the time in years since 1 Jan 2000, then enter the average value of these stocks between 1 Jan 2000 and 1 Jan 2002. $ billion  

[4] 


Your answer will contain a constant symbol "C" or "K". Thus, for example,
if your original GENERAL SOLUTION was "y = x^{2} + K", you would
rewrite the answer here as "1x^{2} +
0y^{2} + 0x
1y + K = 0", and enter
the red numbers below. Scoring : First 4 numbers worth 4 points (no part credit) ; last entry worth a separate 1 point 

x^{2} + y^{2} + x + y + =0 


(Above) Use decimal accurate to 0.01, or enter u if the area is infinite or undefined.  


Scoring : 2 points (above) for correct reduced fraction, one point for an equal but unreduced fraction 
[6] 
Enter decimal numbers (accurate to within 0.01) to form the line which best fits the data points using the
method of leastsquares. If you must consult your text while
answering this question, then you are at risk when writing your paper test later. Scoring : 2½ points (above) for each coefficient (m and b) 



y = x + 
[7] 
(a)(2 pts) Find
f_{x} , f_{y} , f_{xx} ,
f_{xy} , and f_{yy} where
f(x,y) = x^{3}  3xy + y^{3} .
Enter integers below, such as 7, 1, 0, or 3 Scoring : ½ point for each of top 2 derivatives ; 1 point (total) for the bottom 3 derivatives (no part credit) 





(c)(2 pts) Complete the table below using your results in (7a) and (7b) above:
Scoring : ½ point for each CP and each "type" ;
1 point (total) for the middle 4 table columns. Your must get full credit in (7a) and (7b) before credit in (7c) is awarded 


[8](a)(3 pts) Evaluate (showing work) 

(y  2xy) dx  =  x^{3} + y^{3} + x^{2} + y^{2} + xy  
(Above and below) Enter integers to complete the integrals. The algebra and calculus are fairly easy. 
(b)(2 pts) Enter the value of the double integral: 


(y  2xy) dxdy =  
Accuracy to within 0.001 is needed above 
[9] 




(b)(2 pts) Use table entries (above) to write the first 4 terms of the Taylor series for the function f(x) = e^{x}  
f(x) = e^{x} = + x + x^{2} + x^{3} + . . . 
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