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Let f : R3 → R be de?ned by: f(x, y, z) = xy2+ x3z4+ y5z6
a) Compute ~ ∇f(x, y, z) , and evaluate ~ ∇f(2, 1, 1) .
b) Brie?y explain why f must be a di?erentiable function (you just need to "look" at the equations for the partial derivatives).
c) Find D~uf(2, 1, 1) where ~u is a unit vector in the direction of ~v = h4, 3,-1i .
d) Find an equation for the plane which is tangent to the surface de?ned by
xy2+ x3z4+ y5z6= 11
at the point (2, 1, 1) .
e) Use di?erentials to approximate the value of f(2.01, 1.02, 0.97) . Use a calculator to?nd a more accurate value, and compare.
5x-2y+55x=4x
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Determine the centralizer and the order of the conjugacy: 1) Determine the centralizer and the order of the conjugacy class of the matrix [1, 1; 0, 1] in Gl 2 (F 3 ).
a math problem that involves the numbers $112 for 8 hours
I need help on how to do real word problm with unit rates.
SA= Ph+2B L=36 ft W=10 ft H=20 ft P=92 ft B=360 ft
Question A 22 kW, 3-phase, 415 V, 40 A, 50 Hz, 960 rpm, 0.88 PF squirrel cage induction motor drives a pump. The total inertia of the drives system is 1.2 kg-m2. Determine th
An advertising project manager developed the network diagram shown below for a new advertising campagign. In addition, the manager gathered the time information for each activity,
A painter leans a 10-foot ladder against the house she is to paint. The foot of the ladder is 3 feet from the house. How far above the ground does the ladder touch the house? Appro
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