The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x2 - Sy2 - 722 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 2) in the direction towards the point (6, -5, 4). -49 -2100e °C/m (b) In which direction does the temperature increase fastest at P? xi + 5yj + 7zk) (c) Find the maximum rate of increase at P. -18 1.617.10
The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x2 - Sy2 - 722 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 2) in the direction towards the point (6, -5, 4). -49 -2100e °C/m (b) In which direction does the temperature increase fastest at P? xi + 5yj + 7zk) (c) Find the maximum rate of increase at P. -18 1.617.10
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.3: Rates Of Change
Problem 29E: Explain the difference between the average rate of change of y as x changes a to b, and the...
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![The temperature at a point (x, y, z) is given by
T(х, у, 2)
100e-x2 - 5y2 – 722
where T is measured in °C and x, y, z in meters.
(a) Find the rate of change of temperature at the point P(4, -1, 2) in the direction towards the point (6, -5, 4).
49
-2100e
°C/m
(b) In which direction does the temperature increase fastest at P?
(xі + 5уј + 7zk)
(c) Find the maximum rate of increase at P.
-18
1.617· 10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18bd15f3-e082-4552-ab8c-65f456c47ba6%2F6d5e4945-e465-4e68-9bac-121a7599424d%2F1po3ktj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The temperature at a point (x, y, z) is given by
T(х, у, 2)
100e-x2 - 5y2 – 722
where T is measured in °C and x, y, z in meters.
(a) Find the rate of change of temperature at the point P(4, -1, 2) in the direction towards the point (6, -5, 4).
49
-2100e
°C/m
(b) In which direction does the temperature increase fastest at P?
(xі + 5уј + 7zk)
(c) Find the maximum rate of increase at P.
-18
1.617· 10
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