#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

Q1: Let a := 5th digit of your RUID; b := 2nd digit of your RUID
Let f(x, y) := x^a + bx^(2a)y^3

A1: a = 0; b = 9
f(x, y) = 1 + 9y^3
f_x(x, y) = not possible
f_y(x, y) = 27y^2


Q2: W/ a & b as above, fix f_x(z(,x y)) & f_y(z(x, y)) if x, y, & z are related by the eq.: x^a * y^2 * z^b + x^2 * y^(3b) * z^3 = exp(x * y * z)

A2: f_x(z(,x y)): x^a * y^2 * z^b + x^2 * y^(3b) * z^3 = exp(x * y * z)
f_y(z(x, y)): x^a * y^2 * z^b + x^2 * y^(3b) * z^3 = exp(x * y * z)


Q3: Do the second part, find f_y(1. 1)

A3 (USING MAPLE): 0


Q4: Is the answer the same, is f_y(1, 1) also 0? Could you have predicted it without doing the calculation?

A4: The answer is the same and you could've predicted it without doing the calculation.


Q5: Let a & b be as above. Find the eq. Of the tangent plane to the surface z = x^a + y^b + a*b*x*y at the pt. (1, 1, 2+a*b)

A5: F(x, y, z) = y^9 - z = 0 
Fx: 0  -> Fx(1, 1, 2) = 0
Fy: 9y^8  ->  Fy(1, 1, 2) = 9
Fz: -1  ->  Fz(1, 1, 2) = -1
0(x-1) + 9(y-1) -1(z-2) = 0
9y-9-z+2=0
z=9y-z-7