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
.
R(a, b) = (2b + cosa, 2a + sin b, ab)
Determine the equations for the (a) tangent plane and (b) the normal line to the surface S at the point
(-1,2TT, 0)
Check that the point (−1,−1,1) lies on the given surface. Then, viewing the surface as a level surface for a function f(x,y,z) find a vector normal to the surface and an equation for the tangent plane to the surface at (−1,−1,1)
x^2−3y^2+z^2=−1
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