(a) The accompanying figure shows a surface of revolution that is generated by revolving the curve y = f x in the xy -plane about the x -axis. Show that the equation of this surface is y 2 + z 2 = [ f x ] 2 . (b) Find an equation of the surface of revolution that is generated by revolving the curve y = e x in the xy -plane about the x -axis. (c) Show that the ellipsoid 3 x 2 + 4 y 2 + 4 z 2 = 16 is a surface of revolution about the x-axis by finding a curve y = f x in the xy -plane that generates it.
(a) The accompanying figure shows a surface of revolution that is generated by revolving the curve y = f x in the xy -plane about the x -axis. Show that the equation of this surface is y 2 + z 2 = [ f x ] 2 . (b) Find an equation of the surface of revolution that is generated by revolving the curve y = e x in the xy -plane about the x -axis. (c) Show that the ellipsoid 3 x 2 + 4 y 2 + 4 z 2 = 16 is a surface of revolution about the x-axis by finding a curve y = f x in the xy -plane that generates it.
(a) The accompanying figure shows a surface of revolution that is generated by revolving the curve
y
=
f
x
in the xy-plane about the x-axis. Show that the equation of this surface is
y
2
+
z
2
=
[
f
x
]
2
.
(b) Find an equation of the surface of revolution that is generated by revolving the curve
y
=
e
x
in the xy-plane about the x-axis.
(c) Show that the ellipsoid
3
x
2
+
4
y
2
+
4
z
2
=
16
is a surface of revolution about the x-axis by finding a curve
y
=
f
x
in the xy-plane that generates it.
Find an equation for the surface of revolution formed by revolving the curve 2x + 3z = 1 in the xz-plane about the x-axis.
Find parametric equations and a parameter interval for the motion of a particle in the xy-plane that traces the ellipse 16x2 + 9y2 = 144 once counterclockwise.
Chapter 11 Solutions
Calculus Early Transcendentals, Binder Ready Version
University Calculus: Early Transcendentals (4th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY