#ATTENDANCE QUIZ for Dec. 10, SCCII session for Math251(Dr. Z.)
#EMAIL  RIGHT AFTER YOU ATTENDED OR WATCHED THE VIDEO
#BUT NO LATER THAN  Dec. 11, 2020, 8:00PM (Rutgers time)
#THIS .txt FILE (EDITED WITH YOUR ANSWERS)
#TO:
#DrZcalc3@gmail.com
#Subject: sccIIdec10
#with an ATTACHMENT CALLED:
#sccIIdec10FirstLast.txt
#(e.g. sccIIdec10DoronZeilberger.txt)




#LIST ALL THE ATTENDANCE QUESTIONS FOLLOWED BY THEIR ANSWERS

Question 1. 
Compute the line integral Int_C(f*ds) where f=x^2+y^2 and C is the upper semi-circle together with base C= {(x,y): x^2+y^2=1, y>0} UNION {(x,0), -1<x<1) with clockwise orientation 

Answer: 
Pi/2

Question 2. 
Compute the vector field surface integral IntInt_S F.dS
If F=<x^2, y^2, x+z>
And S is the oriented surface
z= 16-x^2-y^2, x>=0, y<0, z>0 POINTING UPWARD
Answer:
46/3

Question 3. 
Find the largest value that the function f(x1,x2,x3,x4)=x1^2*x2*x3*x4
In the plane x1+2*x2+3*x3+4*x4=24

Answer:
f_x1= 2*x1*x2*x3*x4=0
f_x2= x1^2*x3*x4=0
f_x3= x1^2*x2*x4=0
f_x4= x1^2*x3*x2=0
Find critical points which is the location of the maximum value. 
76

Question 4. 
Who is the greatest scientist of all time?

Answer:
Isaac Newton! Modern day scientists have described Newton as “the supreme genius and most enigmatic character in the history of science.”