#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 FOR LECTURE 7
#LET a := 5th digit of YOUR RUID; b := 2nd digit of YOUR RUID
#LET f(x,y) := x^a+bx^(2a)*y^3
#Find THE TWO PARTIAL DERIVATIVES of f(x,y)
f_x(x,y), f_y(x,y)

#ANSWER
a=0, b=0, f(x,y)=1
f_x(x,y)=0,
f_y(x,y)=0

#ATTENDANCE QUESTION #2 FOR LECTURE 7
#With a and b as above, fix f_x z(x,y) and f_y z(x,y) IF x,y,z ARE RELATED BY THE RELATIONSHIP (EQUATION)
#x^a*z^b*y^2+x^2*y^(3b)*x^3=e^(x*y*z)

#ANSWER
y^2+x^5=1
f_x z(x,y)=5^x^4=0
f_y z(x,y)=2y=0

#ATTENDANCE PROBLEM NUMBER 3
#DO THE SECOND PART, FIND f_y(1,1)

#ANSWER
x^2+y^2=xyz+xyz^5
f_y(1,1)=2y=x(y'z+yz')+x(y'z^5+y5z^4z')
2=1+z'+1+5z'
z'=0

#ATTENDANCE PROBLEM NUMBER 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'S STILL 0. I COULD. BECAUSE f_y IS TO REPLACE x BY y FROM f_x.

#ATTENDANCE PROBLEM NUMBER 5
#Let a and b BE AS ABOVE
#Find The Equation of the Tangent Plane to the SURFACE z=x^a+y^b+ab*x^y AT The point (1, 1, 2+ab)

#ANSWER
z=2
f_x z(x,y)=0,
f_y z(x,y)=0
THE EQUATION: z=2