#ATTENDANCE QUIZ for Lecture 7 of Math251(Dr. Z.)
#EMAIL  RIGHT AFTER YOU WATCHED THE VIDEO
#BUT NO LATER THAN  Sept. 28, 2020, 8:00PM (Rutgers time)
#THIS .txt FILE (EDITED WITH YOUR ANSWERS)
#TO:
#DrZcalc3@gmail.com
#Subject: aq7
#with an ATTACHMENT CALLED:
#aq7FirstLast.txt
#(e.g. aq7DoronZeilberger.txt)




#LIST ALL THE ATTENDANCE QUESTIONS FOLLOWED BY THEIR ANSWERS

#ATTENDANCE QUESTION #1:
Let a:= 5th digit of RUID; b:= 2nd digit of RUID

Let f(x,y) := x^5 + 8*x^10*y^3
Find the two partial derivatives of f(x,y)

#ANSWER:
diff(f(x,y), x) = 5*x^4 + 80*x^9*y^3
diff(f(x,y), y) = x^5 + 24*x^10*y^2

#ATTENDANCE QUESTION #2:
With a and b as above, find f_x (z(x,y)) and f_y (z(x,y)) IF
x,y,z are related by the relationship (EQUATION)
x^5 * y^2 * z^8 + x^2*y^(24)*z^3 = exp(x*y*z)

#ANSWER:
f_x(z(x,y)) = 5*x^4*y^2*8*z^7*z' + 2*x*y^24*3*z^2*z' - z'*e^(x*y*z)
f_x(z(x,y)) = 0
f_y(z(x,y)) = 0

#ATTENDANCE QUESTION #3:
Do the second part, find f_y(1,1)

#ANSWER:
Diff. w.r.t to y
(x^2 + y^2)' = (x*y*z + x*y*z^5)'
2y = x*(y*z)' + x*(y*z^5)'
2x = x*(z+y*z') + x*(z^5 + y^4*z^3*z')
2 = 2 + 5*z'
0 = 5*z'
z' = 0

#ATTENDANCE QUESTION #4:
Is the answer the same, is f_y(1,1) also 0?
Could you have predicted it without doing the calculation

#ANSWER:
Yes it is the same. I could have predicted it by noticing that x and y were changed but they are the same value!

#ATTENDANCE PROBLEM NUMBER 5
Let a and b be as above
Find the equation of tangent plane to the surface
z = x^0 + y^8 + 0 at the point (1,1,2)

#ANSWER
z = 1 + y^8
The point does lie on the surface
f_x = 0
f_y = 7*y^8
f_x(1,1) = 0
f_y(1,1) = 7
z-2 = 0(x-1) + 7(y-1)
z=7(y-1) + 2
z = 7y - 7 + 2
z = 7y - 5