#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 your RUID
Let 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)

a=0
b=8

Not a valid partial derivative

#Attendance question 2

with a & b as above, fix f_x(z(x,y) and f_y(z(x,y)) IF
x,y,x are related by the relationship (equation)

a=0
b=8

x^a * y^2 * z^b + x^2 * y^(3b) * z^3 = exp(x*y*z)

#Attendance question 3
Do the second part f_y(1,1)

x^2+y^2=(x*y*z+x*y*z^5)
2y=(x*y*z)'+(x*y*z^5)'
2y=x*(y*z)'+x*(x*y*z^5)
2y=x*(y'*z+y*z')+x*(y'*z^4+y*(z^4)')
2y=x*(z+y*z')+y*(z^4+x*4*z^3*z')

2*1=1*(1+1z')+1*(1^4+1*4*1^3*z')
2=1+z' + 1+4z
2=2 + 5*z'
0=5*z'
z'=0

#Attendance question 4
Is F_y(1,1) Also 0?
Yes it is also 0, you can predict it because x and y are both 0 and z is related to the values x and y

#Attendance 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)=(1,1,2)
z=x^0+y^8+0
z_0=f(1,1)=2
f_x=1
f_y=1

z-2=1(x-1)+1(y-1)
z=x+y-4