Question

The temperature at a point (x, y, z) is given by T(x, y, z) = 100e^(−x^2 − 3y^2 − 9z^2) where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(2, −1, 2) in the direction towards the point (5, −2, 3). (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.

Answer #1

The temperature at a point (x, y, z) is given by T(x, y, z) =
400e−x2 − 5y2 − 9z2 where T is measured in °C and x, y, z in
meters.
(a) Find the rate of change of temperature at the point P(2, −1,
2) in the direction towards the point (3, −5, 6). °C/m
(b) In which direction does the temperature increase fastest at
P?
(c) Find the maximum rate of increase at P.

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errors in this problem; just try to keep track of what needs to be
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which direction (unit vector) does the temperature...

The temperature at a point (x,y,z) is given by
T(x,y,z)=200e−x2−y2/4−z2/9, where Tis measured in degrees celcius
and x,y, and z in meters. There are lots of places to make silly
errors in this problem; just try to keep track of what needs to be
a unit vector.
Find the rate of change of the temperature at the point (0, 1, -2)
in the direction toward the point (-1, -2, 5).
In which direction (unit vector) does the temperature increase the...

The temperature at a point (x, y, z) is given by T(x, y, z) =
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The temperature T of a flat sheet, at the point (?x, y) ?, is
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?, from the point P (? − 1,2) ?. b) Calculate the highest rate of
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The temperature on a surface can be described by the equation
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f(x, y, z) = x y2 z3 and consider the
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(a) Find the directional derivative of f at P in the direction
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(c) What is the maximal rate of increase of f at P?

Given the level surface S defined by f(x, y, z) = x −
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Find the equation of the tangent plane to the surface S at the
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Find the derivative of f at P0in the direction of
r(t) =< 3, 6, −2 >
Find the direction and the value of the maximum rate of change
greatest increase of f at P0;
(d) Find the parametric equations of the...

The temperature in degrees Celsius on the surface of a metal
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T (x, y) = 20 − 4x^(2) − y^(2) where x and y are measued in
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In which direction from the point (2, −3) does the temperature
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What is this rate of increase in that direction?
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please show me the steps
Suppose the temperature at (x, y, z) is given by T = xy +
sin(yz). In what direction should you go from the point (1, 1, 1)
to decrease the temperature as quickly as possible? What is the
rate of change of temperature in this direction?

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