#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
Let b = 2nd digit of RUID

Let f(x,y) = x^a + b*x^(2*a) * y^3
Find the two partial derivatives of f(x,y)

ANSWER 1:
RUID: 201001195

f(x,y) = 1 + 0*1

f_x = 0
f_y = 0

ATTENDANCE QUESTION 2:
With a and b as above, fix f_z (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^2(3*b)*z^3 = exp(x*y*z)

ANSWER 2:

I don’t know how to isolate for z.

ATTENDANCE QUESTION 3:
If z = f(x,y) is given by the equation:
x^2+y^2 = x*y*z + x*y*z^5
Find f_y(1,1)

ANSWER 3:

(x^2+y^2)’ = (x*y*z + x*y*z^5)’
2*y = (x*y*z)’ + (x*y*z^5)’
2*y = x*(y*z)’ + x*(y*z^5)’
2*y = x*(z + y*z’) + x*(z^5 + y^5*z^5*z’)

Z’ = 0
f_y(1,1) = 0

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

ANSWER 4:
Yes the answer is the same, you could have predicted this because the only thing that changes is x and y switch.

ATTEDANCE QUESTION 5:
Let a and b be as above

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)

ANSWER 5:
RUID: 201001195

(1,1,2)
A = 0
B = 0

Z = 1 + 1 + 0
Z = 2

W = z - 2
f_x = 0
f_y = 0
f_z = 1

0 = (0)(1)(x-1) + (0)(1)(y-1) + (1)(2)(z-2)
0 = 2z-2

Z = 1