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Evaluate and classify the critical point of the function f(x, y) = xy
If A~ = 2yˆi - zˆj + 3xkˆ
(i). Find the unit vectors eˆr, eˆθ and eˆz of a cylindrical coordinates in termsof ˆi, ˆj and kˆ.
(ii). Solve for ˆi, ˆj and kˆ in terms of eˆr, eˆθ and eˆz
(iii). Represent the vector A~ in cylindrical coordinates and determine Ar, Aθ
and Az
(a) Find the linearization of f(x, y) = e^(x) cos y at the point (0, π/2)
2. f(x,y,z)= 1/(√ (4-x^2-y^2-z^2)
all 77 rooms in a motel will be rented each night if the maanager charges $39 or less per room. if he charges $(39 +y) per room then 2y rooms will remain vacant. If each rented room costs the manager $5 per day and each unrented room $3 per day in overhead , how much should the manager charge per room to maximize his profit. find;
i) no of rented rooms
ii)the revenue
iii)total cost in overhead
x→∞
Determine the first order partial derivative of the following function:
"F(x,y)=\\int_{y}^x cos(e^t)dt"
2−y
2
.
D
(x + 2y)dA, where D is the region bounded by the parabolas
y = x
2
, and y = 1 + x
directional derivatives of xy2+yz3 at (1,-1,1) along i+2j+2k
