The temperature at a point (x, y, z) is given by 60 T(x, y, z) 1+ a? + 3y? + 2z² ' where T is measured in degrees Celsius and æ, y, z in metres. (a) The gradient vector at a general point (x, y, z) is given by VT(x, y, z) = ). (b) Find the directional derivative of the temperature T at the point (1, 0, 0) in the direction of the vector (4, 3, 0). (If necessary, round to three decimal places.) Answer (c) What is the maximal rate of increase of the temperature T at the point (1, 0, 0)? (If necessary, round to three decimal places.) Answer (d) In which direction should we move from the point (1, 0, 0) so that the temperature T stays constant? (You may assume that the directions in all of the options below are nonzero unit vectors.) OIn any direction as long as it is a unit vector. OIn the same direction as VT(1,0, 0). OIn the opposite direction as VT(1,0,0). O In a direction that is perpendicular to VT(1,0, 0). O None of the above.
The temperature at a point (x, y, z) is given by 60 T(x, y, z) 1+ a? + 3y? + 2z² ' where T is measured in degrees Celsius and æ, y, z in metres. (a) The gradient vector at a general point (x, y, z) is given by VT(x, y, z) = ). (b) Find the directional derivative of the temperature T at the point (1, 0, 0) in the direction of the vector (4, 3, 0). (If necessary, round to three decimal places.) Answer (c) What is the maximal rate of increase of the temperature T at the point (1, 0, 0)? (If necessary, round to three decimal places.) Answer (d) In which direction should we move from the point (1, 0, 0) so that the temperature T stays constant? (You may assume that the directions in all of the options below are nonzero unit vectors.) OIn any direction as long as it is a unit vector. OIn the same direction as VT(1,0, 0). OIn the opposite direction as VT(1,0,0). O In a direction that is perpendicular to VT(1,0, 0). O None of the above.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The temperature at a point (x, y, z) is given by
60
T(x, y, z)
1+ x2 + 3y2 + 2z2'
where T is measured in degrees Celsius and æ, y, z in metres.
(a) The gradient vector at a general point (x, y, z) is given by
VT(x, y, z) =
).
(b) Find the directional derivative of the temperature T at the point (1, 0, 0) in the
direction of the vector (4, 3, 0). (If necessary, round to three decimal places.)
Answer =
(c) What is the maximal rate of increase of the temperature T at the point (1, 0, 0)? (If
necessary, round to three decimal places.)
Answer
(d) In which direction should we move from the point (1, 0, 0) so that the temperature
T stays constant? (You may assume that the directions in all of the options below are
nonzero unit vectors.)
O In any direction as long as it is a unit vector.
O In the same direction as VT(1, 0, 0).
O In the opposite direction as VT(1,0,0).
OIn a direction that is perpendicular to VT(1, 0, 0).
O None of the above.
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