Answer to Question #72283 in Calculus for chisomo

Question

1. Find the indicated derivatives:
a) u =
x+y
y+z
, x = p + r + t, y = p − r + t, z = p + r − t;
∂u
∂r .
b) y
5 + x
2
y
3 = 1 + yex
2
;
dy
dx .
c) ln(x + yz) = 1 + xy2
z
3
; ∂z/∂y
2. Let f(x, y) = x
2
y + x
3
y
2 and suppose you dont know what φ(t) = (x(t), y(t)) is, but you
know φ(2) = (1, 1), dx
dt (2) = 3, and dy
dt (2) = 1. Find the derivative of f(φ(t)) when t = 2.
3. Show that the following functions are functionally dependent and find a relation connect￾ing them:
f(x, y, z) = x + y + z, g(x, y, z) = x
2 + y
2 + z
2
, h(x, y, z) = xy + yz + xz
4. Find the local maxima, minima, and saddles of the functions h(x, y) = (2x−x
2
)(2y −y
2
).
5. Find the largest volume of a box with an open top, and surface area 100m2
.
6. Find the absolute minimum of f(x, y) = x
2 + y
2 + 2y − 1 on D = {(x, y)|x
2 +
y
2
4 ≤ 1}

Answer 1

Dear chisomo, your question requires a lot of work, which neither of our experts is ready to perform for free. We advise you to convert it to a fully qualified order and we will try to help you. Please click the link below to proceed: Submit order