#ATTENDANCE QUIZ for Lecture 8 of Math251(Dr. Z.)
#EMAIL  RIGHT AFTER YOU WATCHED THE VIDEO
#BUT NO LATER THAN  Oct. 1, 2020, 8:00PM (Rutgers time)
#THIS .txt FILE (EDITED WITH YOUR ANSWERS)
#TO:
#DrZcalc3@gmail.com
#Subject: aq8
#with an ATTACHMENT CALLED:
#aq8FirstLast.txt
#(e.g. aq8DoronZeilberger.txt)




#LIST ALL THE ATTENDANCE QUESTIONS FOLLOWED BY THEIR ANSWERS

Q1.
Let a:= 5th digit of RUID b:= 2nd digit of RUID
Let f(x,y):= x^a +b*a^(2*a)*y^3
Find partial derivatives of f(x,y)

A1.
a=0 
b=9
f(x,y)=x^0 + 9*0^(2*0)*y^3
f_x=0+0=0
f_y=0+0=0


Q2.
With same a=0 and b=9 as above
find implicit of both x and y
x^a * y^2 * z^b + x^2*y^(3*b)*z^3=exp(x*y*z)

A2.
x: y^2(9z^8dz/dx)+y^(27)(x^2*3z^2dz/dx+2x*z^3)=exp(yxdz/dx+yz)
y:(y^2*9z^8dz/dy+2y*z^9)+x^2(y^27*3z^2*dz/dy+27y^26*z^3)=exp(xydz/dy+xz)


Q3.
Find f_y(1,1) of
x^2+y^2 = x*y*z + x*y*z^5 

A3.
2y=x(ydz/dy+z) + x(y*5z^4dz/dy+1*z^5)
2=(dz/dy)+1 + (5dz/dy)+1
Dz/dy=0


Q4.
Is f_y(1,1)=0

A4.
It is. The slopes are not the same so I cannot tell

Q5.
Let a and b be as above
Find equation of tangent plane to surface
z= x^a + y^b +a*b*x*y At point (1,2,2+a*b)

A5.
z= x^0 + y^9 + 0*x*y At point (1,2,2)
2= 1+2^9+0 <—DNE