function R (w, v) =< √√w · log7 w · sin v, where w> 0 and 0 ≤ v ≤ 2π.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 34E
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If the tangent plane to the level
surface of F(x, y, z) at the point
Po = (xo, Yo, zo) is also tangent to
a level surface of G(x, y, z) at
P₁ = (xo, Yo, zo)
Ро
then
▼F(x0, Yo, ²0) = ▼G(xo, Yo, zo)
Transcribed Image Text:If the tangent plane to the level surface of F(x, y, z) at the point Po = (xo, Yo, zo) is also tangent to a level surface of G(x, y, z) at P₁ = (xo, Yo, zo) Ро then ▼F(x0, Yo, ²0) = ▼G(xo, Yo, zo)
3
If the curve y = √z · log7 z, for
z > 0, on the yz-plane is revolved
about the z-axis, the surface
can be defined by the
generated
vector-valued
function
3
R (w, v) =< ³/w · log7 w · sin v,
where w> 0 and
0 ≤v≤ 2π.
< υ
Transcribed Image Text:3 If the curve y = √z · log7 z, for z > 0, on the yz-plane is revolved about the z-axis, the surface can be defined by the generated vector-valued function 3 R (w, v) =< ³/w · log7 w · sin v, where w> 0 and 0 ≤v≤ 2π. < υ
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