Looking ahead—tangent planes Consider the following surfaces f ( x, y, z ) = 0, which may be regarded as a level surface of the function w = f ( x, y z ) . A point P ( a. b, c ) on the surface is also given. a. Find the ( three-dimensional) gradient off and evaluate it at P b. The set of all vectors orthogonal to the gradient with their tails at P form a plane. Find an equation of that plane ( soon to be called the tangent plane ) . 73. f ( x , y , z ) = e x + y − z − 1 = 0 ; P ( 1 , 1 , 2 )
Looking ahead—tangent planes Consider the following surfaces f ( x, y, z ) = 0, which may be regarded as a level surface of the function w = f ( x, y z ) . A point P ( a. b, c ) on the surface is also given. a. Find the ( three-dimensional) gradient off and evaluate it at P b. The set of all vectors orthogonal to the gradient with their tails at P form a plane. Find an equation of that plane ( soon to be called the tangent plane ) . 73. f ( x , y , z ) = e x + y − z − 1 = 0 ; P ( 1 , 1 , 2 )
Solution Summary: The author explains that the gradient of f(x,y,z)=ex+y-z
Looking ahead—tangent planesConsider the following surfaces f(x, y, z) = 0, which may be regarded as a level surface of the function w = f(x, y z). A point P(a. b, c) on the surface is also given.
a.Find the (three-dimensional) gradient off and evaluate it at P
b.The set of all vectors orthogonal to the gradient with their tails at P form a plane. Find an equation of that plane (soon to be called the tangent plane).
73.
f
(
x
,
y
,
z
)
=
e
x
+
y
−
z
−
1
=
0
;
P
(
1
,
1
,
2
)
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.
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