Let T(x,y) denote the temperature at location (x,y). You are given the following information. • The...
Let T(x,y) denote the temperature at location (x,y). You are given the following information.
• The rate of change of T at the point A(1,2) in the direction ~ w = ˆ i + ˆ j is √8.
• The rate of change of T at the point A(1,2) in the direction ~ v = 4ˆ i −3ˆ j is 6. • The temperature at A(1,2) is 20.
(a) From the point A(1,2), in which direction would you head to cool off most rapidly?
(b) What is the minimum rate of change of temperature at point A(1,2)?
(c) Estimate the temperature at the point (0.97,2.02) to two decimal places.
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Let T(x,y) denote the temperature at location (x,y). You are
given the following information.
• The...
(20p) The temperature function T(x,y) is defined as T(x,y) = cos(-) at a specified location. Here...
(20p) The temperature function T(x,y) is defined as T(x,y) = cos(-) at a specified location. Here x denotes the north direction and y denotes the east direction. So that Tx is the rate of change of the temperature with respect to distance if we travel north direction and Ty is the rate of change of the temperature with respect to distance if we travel east direction. Find the rate of change of temperature at the point ( 1) when we...
3. Let X denote the temperature (°C) and let Y denote the time in minutes that...
3. Let X denote the temperature (°C) and let Y denote the time in minutes that it takes for the diesel engine on an automobile to get ready to start. Assume that the joint density for (X,Y) is given by fxy(x, y) = c(4x + 2y + 1),0 < x < 40,0 < y = 2 (a) Find the value of c that makes this joint density legitimate. (b) Find the probability that on a randomly selected day the air...
(a) The temperature T(x, y) at a point (x, y) on a plate is given by T(x, y) = 16 − x 2 − 2y 2 . ...
(a) The temperature T(x, y) at a point (x, y) on a plate is given by T(x, y) = 16 − x 2 − 2y 2 . i. What is the direction of greatest increase in temperature at the point P = (1, 3)? [3 marks] ii. What are the directions of zero change in temperature at the point P? [4 marks] iii. Find the path of greatest increase in temperature from the point P to the point of maximum...
(8 points) The temperature at a point (x, y, z) is given by T(x, y, z)...
(8 points) The temperature at a point (x, y, z) is given by T(x, y, z) = 1300e-x-2y-2? where T is measured in °C and x, y, and z in meters. 1. Find the rate of change of the temperature at the point P(2, -1, 2) in the direction toward the point Q(3,-3,3). Answer: Dp S(2.-1, 2) = 2. In what direction does the temperature increase fastest at P? Answer: 3. Find the maximum rate of increase at P. Answer:
The temperature at a point (x, y, z) is given by T(x, y, z) = 100e?x2 ? 3y2 ? 7z2 where T is...
The temperature at a point(x, y, z)is given byT(x, y, z) = 100e?x^2 ? 3y^2 ? 7z^2where T is measured in °C andx, y, zin meters.(a) Find the rate of change of temperature at the point P(2, ?1, 2) in the direction towards the point(3, ?2, 3).(b) In which direction does the temperature increase fastest at P?(c) Find the maximum rate of increase at P.
The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x2...
The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x2 - 5y2 - 722 where Tis measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P12,-1, 3) in the direction towards the point (5, -3, 6). °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.
Problem 3. (1 point) The temperature at a point (X,Y,Z) is given by T(x, y, z)...
Problem 3. (1 point) The temperature at a point (X,Y,Z) is given by T(x, y, z) = 200e-x=y+14–2–19, where T is measured in degrees Celsius 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 (-1, 1,-1) in the direction toward the point (-4,-5, -5). In which direction...
#2 #3 #4 #5 please help me with the TRUE or FALSE Given Vf(1,2, 0) =...
#2
#3
#4
#5
please help me with the TRUE or FALSE
Given Vf(1,2, 0) = 3i +j -4k, at point (1,2, 0) the directional derivative in the direction <1, 2, -2> is... 5 None of the three. 13 3 13 Considerf (x, y) xe-2* at (x, y) (1,2) Which of the following is FALSE? To estimate f(0.9, 2. 2), let dx = -0. 1 and dy 0.2, calculatedf(1,2), and subtract it from f(1,2). f(1, 2) 1 None of the...
Let g(x, y, z) = x2 + xy + xyz?. (a) Find the gradient of g....
Let g(x, y, z) = x2 + xy + xyz?. (a) Find the gradient of g. (b) Find the rate of change of g at the point (1,-1,2) in the direction of the vector v = (8,4,-1).
4 marks] Find a unit vector in the direction in which J(x,y) - V marks Find a unit vector in the ...
4 marks] Find a unit vector in the direction in which J(x,y) - V marks Find a unit vector in the direction in which f(r, decress most rapidly at P(3, 1); and find the rate of change of at P in that direction.
4 marks] Find a unit vector in the direction in which J(x,y) - V marks Find a unit vector in the direction in which f(r, decress most rapidly at P(3, 1); and find the rate of change...
(20p) The temperature function T(x,y) is defined as T(x,y) = cos(-) at a specified location. Here x denotes the north direction and y denotes the east direction. So that Tx is the rate of change of the temperature with respect to distance if we travel north direction and Ty is the rate of change of the temperature with respect to distance if we travel east direction. Find the rate of change of temperature at the point ( 1) when we...
3. Let X denote the temperature (°C) and let Y denote the time in minutes that it takes for the diesel engine on an automobile to get ready to start. Assume that the joint density for (X,Y) is given by fxy(x, y) = c(4x + 2y + 1),0 < x < 40,0 < y = 2 (a) Find the value of c that makes this joint density legitimate. (b) Find the probability that on a randomly selected day the air...
(8 points) The temperature at a point (x, y, z) is given by T(x, y, z) = 1300e-x-2y-2? where T is measured in °C and x, y, and z in meters. 1. Find the rate of change of the temperature at the point P(2, -1, 2) in the direction toward the point Q(3,-3,3). Answer: Dp S(2.-1, 2) = 2. In what direction does the temperature increase fastest at P? Answer: 3. Find the maximum rate of increase at P. Answer:
The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x2 - 5y2 - 722 where Tis measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P12,-1, 3) in the direction towards the point (5, -3, 6). °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.
Problem 3. (1 point) The temperature at a point (X,Y,Z) is given by T(x, y, z) = 200e-x=y+14–2–19, where T is measured in degrees Celsius 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 (-1, 1,-1) in the direction toward the point (-4,-5, -5). In which direction...
#2
#3
#4
#5
please help me with the TRUE or FALSE
Given Vf(1,2, 0) = 3i +j -4k, at point (1,2, 0) the directional derivative in the direction <1, 2, -2> is... 5 None of the three. 13 3 13 Considerf (x, y) xe-2* at (x, y) (1,2) Which of the following is FALSE? To estimate f(0.9, 2. 2), let dx = -0. 1 and dy 0.2, calculatedf(1,2), and subtract it from f(1,2). f(1, 2) 1 None of the...
Let g(x, y, z) = x2 + xy + xyz?. (a) Find the gradient of g. (b) Find the rate of change of g at the point (1,-1,2) in the direction of the vector v = (8,4,-1).
4 marks] Find a unit vector in the direction in which J(x,y) - V marks Find a unit vector in the direction in which f(r, decress most rapidly at P(3, 1); and find the rate of change of at P in that direction.
4 marks] Find a unit vector in the direction in which J(x,y) - V marks Find a unit vector in the direction in which f(r, decress most rapidly at P(3, 1); and find the rate of change...
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