#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, 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)

Answer:

f'x(x, y) = 0
f'y(x, y) = 27y^2

Attendance Question 2

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

Answer:

f_x(z(x, y)) = 2 * y^27 * z^3 * x
f_y(z(x, y)) = 2yz^9 + 27 * x^2 * z^3 * y^26

Attendance Question 3

Do the second part find f_y(1,1)

Answer:

f_y(1,1) = 0

Attendance Question 4

Is the answer the same? Is f_y(1,1) also 0? 
Could you have predicted it without doing the calculation?

Answer:

Yes, the answer is the same. You could predict it without doing the calculation since x and y are equal.

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 + abxy at the point (1, 1, 2+ab)

Answer:

f_x = d/dx(y^9 + 1) = 0			f_x(1, 1, 2) = 0
f_y = d/dy(y^9 + 1) = 9y^8		f_y(1, 1, 2) = 9

z-2 = 0(x-1) + 9(y-1)
z = 9y-7