Question

Consider the funtion T(x,y)=2xy-y^2(°C) which determines the temperature for a metallic circular plate centered at the origin and radius = 5, Explain why there's no direction in which the rate of change of temperature in the point P(1,-1) is equals to 5°C. consider units are cm.

Answer #1

Consider the vector field below: F ⃗=〈2xy+y^2,x^2+2xy〉 Let C be
the circular arc of radius 1 starting at (1,0), oriented counter
clock wise, and ending at another point on the circle. Determine
the ending point so that the work done by F ⃗ in moving an object
along C is 1/2.

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The temperature T of a flat sheet, at the point (?x, y) ?, is
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T (?x, y) ? ? x ^ 3 - 2xy + ? 2y ^ 22. a) Determine the rate of
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?, from the point P (? − 1,2) ?. b) Calculate the highest rate of
temperature growth from P (? − 1,2) ?, as well as the direction in
which it...

The temperature on a surface can be described by the equation
T(x, y, z) = 2xy + xy2 z + 12e 2z . Use this function to answer the
following questions. Remember to clearly organize your work and
indicate your final answer.
(a) Find the direction you should head to achieve the greatest
rate of change in temperature at any point.
(b) Find the direction you should head to achieve the greatest
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The temperature in degrees Celsius on the surface of a metal
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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?
c.∗ How much greater is the rate of increase from (2, −3) in the
direction of
the gradient, then the rate of change in the direction of...

A circular loop of radius R1 lies in the x − y plane, centered
on the origin, and has a current i running through it clockwise
when viewed from the positive z direction. A second loop with
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parallel to the first.
1. If the second loop is centered at the point z = R1, what must
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The temperature at a point (x, y, z) is given by T(x, y, z) =
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The temperature at a point (x, y, z) is given by T(x, y, z) =
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(b) In which direction does the temperature increase fastest at
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(c) Find the maximum rate of increase at P.

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The temperature at a point (x, y, z) is given by T(x, y, z) =
10e^(− 2x2 − y2 − 3z2). In which direction does the temperature
increase fastest at the point (2, 1, 3)? Express your answer as a
UNIT vector.

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