6. Sketch the surface described by the parameterization r(u, v) = (u, v cos(u), v sin(u)) for 0 ≤ u≤ 8π and 1 ≤ v ≤ 3. Find the area of this surface. Hint: you may use that the function =x√1 + x² +ln(x + √√1+x²) satisfies f'(x) = 2√1+x². f(x) =

6. Sketch the surface described by the parameterization r(u, v) = (u, v cos(u), v sin(u)) for 0 ≤ u≤ 8π and 1 ≤ v ≤ 3. Find the area of this surface. Hint: you may use that the function =x√1 + x² +ln(x + √√1+x²) satisfies f'(x) = 2√1+x². f(x) =

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...

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Question

6. Sketch the surface described by the parameterization
r(u, v) = (u, v cos(u), v sin(u))
for 0 ≤ u ≤ 8π and 1 ≤ v ≤ 3. Find the area of this surface. Hint: you may use that the function
f(x)=x√√1+x² + ln(x + √1 + x²)
satisfies f'(x) = 2√√/1 + x².

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