Lateral Surface Area In Exercises 65-72, find the area of the lateral surface (see figure) over the curve C in the xy-plane and under the surface z = f ( x , y ) where Lateral surface area = ∫ C f ( x , y ) d s . f ( x , y ) = h , C: line from (0, 0) to (3, 4)
Lateral Surface Area In Exercises 65-72, find the area of the lateral surface (see figure) over the curve C in the xy-plane and under the surface z = f ( x , y ) where Lateral surface area = ∫ C f ( x , y ) d s . f ( x , y ) = h , C: line from (0, 0) to (3, 4)
Solution Summary: The author calculates the value of the lateral surface area over the curve C in xy -plane and under the given surface.
Lateral Surface Area In Exercises 65-72, find the area of the lateral surface (see figure) over the curve C in the xy-plane and under the surface
z
=
f
(
x
,
y
)
where Lateral surface
area
=
∫
C
f
(
x
,
y
)
d
s
.
Check that the point (-2, 2, 4) lies on the surface
cos(x + y) = exz+8
(a) View this surface as a level surface for a function
f(x, y, z). Find a vector normal to the surface at the
point (-2, 2, 4).
(b) Find an implicit equation for the tangent plane to the
surface at (-2, 2, 4).
Identify all extrema of the function f(x,y)=x³+y³-3x-12y +20 on the plane and
characterize them.
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