#ATTENDANCE QUIZ for Dec. 7 SCCII session for Math251(Dr. Z.)
#EMAIL  RIGHT AFTER YOU ATTENDED OR WATCHED THE VIDEO
#BUT NO LATER THAN  Dec. 8, 2020, 8:00PM (Rutgers time)
#THIS .txt FILE (EDITED WITH YOUR ANSWERS)
#TO:
#DrZcalc3@gmail.com
#Subject: sccIIdec7
#with an ATTACHMENT CALLED:
#sccIIdec7FirstLast.txt
#(e.g. sccIIdec7DoronZeilberger.txt)


#LIST ALL THE ATTENDANCE QUESTIONS FOLLOWED BY THEIR ANSWERS

Question 1. 
Use the divergence theorem to find IntInt(F*dS) if r[I]:= be the I-th digit of your RUID (if zero make it 1) F=<r[3]*x-r[5]*y+z, r[6]*x+z, x+r[9]*z> 
Let S be the surface of the cube [0,3]x[0,4]x[0,5]
With the normal pointing inwards

Answer:
F= <6x - y + z, x + z, x + 2z>


Question 2. 
By converting to polar coordinates and not using maple
Int (from x=0 to x=3)Int(y=-sqrt(9-x^2) to y=0 (x^2+y^2)^3*x*y * dy * dx

Answer: 
2

Question 3. Investigate whether the following limit exists
(I) using the experimental 
(ii) fully mathematical approach 
Limit of (x+2*y+3*z-6)/(3*x+2*y+z-6)
Answer:
If it is the limit going to the point (0,0,0) then the limit is 1. Experimentally we find this value by plugging in the point (0,0,0), but the full mathematical approach involves plugging in y=cx and solving to see if the equation relies on the slope c

Question 4. 
Compute the line integral of Int_C f ds
If f(x,y,z)= x+y+z
Answer: 
Int(o to 1) (3t)dt= 3/2