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)
Find the maximum rate of change of f at the given point and the direction in which it occurs.
f(x, y) =8xy2, (5,-7)
maximum rate of change
direction vector
Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0 ≤ t ≤ 5.
Please explain your steps. Thank you.
Chapter 13 Solutions
Calculus Early Transcendentals, Binder Ready Version
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