#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. THE FIRST ATTENDANCE QUESTION WAS: Let a=5th digit of your RUID; b=2nd digit of your RUID. Let f(x,y) = x^a + b*x^(2a)*y^3.
#Find the two partial derivatives of f(x,y).

A1. MY ANSWER TO THE FIRST ATTENDANCE QUESTION IS: 

#Step 1: a = 0, b = 9:  f(x,y) = 1 + 9*x^(0)*y^3 = 1 + 9y^3

#Step 2: df/dy = 27y^2  (cant do 2 partial because there is only the y variable) 


Q2. THE  SECOND ATTENDANCE QUESTION WAS: 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^a * y^2 * z^b + x^2 * y^(3*b) * z^3 = exp(x*y*z)

A2. MY ANSWER TO THE  SECOND ATTENDANCE QUESTION IS:y^2*z^9 + 2x*y^27*z^3 = exp(xyz)*xz  AND  2y*z^9 + x^2*27*y^26*z^3 = exp(xyz)*xz

#Step 1: 1 * y^2 * z^9 + x^2 * y^(27) * z^3 = exp(x*y*z)

#Step 2: With respect to x: y^2*z^9 + 2x*y^27*z^3 = exp(xyz)*xz

#Step 3: With respect to y: 2y*z^9 + x^2*27*y^26*z^3 = exp(xyz)*xz

Q3. THE  THIRD ATTENDANCE QUESTION WAS: Do the second part, find f_y(1,1)

A3. MY ANSWER TO THE  THIRD ATTENDANCE QUESTION IS: 1

#Step 1: z' = 0 z = 1. f_y(1,1) = 2y - x - 1

#Step 2: f_y(1,1) = 2(1) - 1 - 1 = 0

Q4. THE FOURTH ATTENDANCE QUESTION WAS: Is the answer the same, if f_y(1,1) also 0? Could you have predicted it without doing the calculation?

A4. MY ANSWER TO THE FOURTH ATTENDANCE QUESTION IS: Yes, the answer stays the same. f_y(1,1) is also 0. It could have been predicted without doing calculations. 

Q5. THE FIFTH ATTENDANCE QUESTION WAS: Let a and b be as avove, find the equation of the tangent plane to the surface:
# z = x^a + y^b + a*b*x*y at the point (1,1,2+a*b)

A5. MY ANSWER TO THE FIFTH ATTENDANCE QUESTION IS: z = -9y + 11

#Step 1: a = 0 b = 9

#Step 2: z = 1 + y^9 at the point (1,1,2)

#Step 3: Fx = 0. Fy = 9y^8 and plug in 1 which gets Fy(1,1,2) = 9, Fz = 1

#Step 4: 0 + 9y - 9 + z - 2

#Step 5: z = -9y + 11