The temperature (in degrees Celsius) at a point x , y on a metal plate in the x y -plane is T x , y = x y 1 + x 2 + y 2 (a) Find the rate of change of temperature at 1 , 1 in the direction of a = 2 i − j . (b) An ant at 1 , 1 wants to walk in the direction in which the temperature drops most rapidly. Find a unit vector in that direction.
The temperature (in degrees Celsius) at a point x , y on a metal plate in the x y -plane is T x , y = x y 1 + x 2 + y 2 (a) Find the rate of change of temperature at 1 , 1 in the direction of a = 2 i − j . (b) An ant at 1 , 1 wants to walk in the direction in which the temperature drops most rapidly. Find a unit vector in that direction.
The temperature (in degrees Celsius) at a point
x
,
y
on a metal plate in the
x
y
-plane
is
T
x
,
y
=
x
y
1
+
x
2
+
y
2
(a) Find the rate of change of temperature at
1
,
1
in the direction of
a
=
2
i
−
j
.
(b) An ant at
1
,
1
wants to walk in the direction in which the temperature drops most rapidly. Find a unit vector in that direction.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Find the maximum rate of change of f(x, y)
Maximum rate of change: 2/5
In(x? + y?) at the point (-4, -3) and the direction in which it occurs.
Direction (unit vector) in which it occurs:
-8/25
-6/25
出)
Subtracting the two equations, find a vector equation for the curve of intersection between y= 4x2+(3/4)z2 and y-1= 3x2+(1/2)z2 for x>0. Find and simplify the tangential component of acceleration for your curve.
Let f(x, y) = xex - y and P = (9, 81).
(a) Calculate || Vfp||-
||Vfel| =|
(b) Find the rate of change of f in the direction Vfp.
(c) Find the rate of change of f in the direction of a vector making an angle of 45° with Vfp.
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