Difference between revisions of "Calculus III Advanced (Course) (11.6) (Homework)"
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Latest revision as of 20:07, 15 April 2017
Contents
Section 11.6 Homework
From Calculus 10e by Larson and Edwards, p. 802. Exercises 1, 2, 3, 4, 5, 6, 10, 16, 32, 44.
Exercises 11.6.1-6 Match the Equation with its Graph
Solution
1. c, 2. e, 3. f, 4. b, 5. d, 6. e.
Exercise 11.6.10 Sketching a Surface in Three Dimensions
- \(y^{2}+z=6\)
Solution
Exercise 11.6.16 Sketching a Quadric Surface
Describe and sketch
- \( -8x^{2}+18y^{2}+18z^{2}=2 \)
Solution One-sheet Hyperboloid
Exercise 11.6.32 Find the Equation for a Rotated Surface
Curve Equation | \(z=3y \) |
Coordinate Plane | \(yz\)-plane |
Axis of Revolution | \(y\)-axis |
Solution
To find an equation for the surface form by revolving the graph for \(z=3y\) about the \(y\)-axis, solve for \(z\) in \(y\) terms.
- \(z=3y=r(y)\)
The equation for the surface is
- \( 0x^{2}+z^{2}=[r(y)]^{2} \) Revolved about the \(y\)-axis
- \( z^{2}=(3y)^{2} \) Substitute \(3y\) for \(r(y)\)
- \( z^{2}=9y^{2} \) Equation for the surface.
Exercise 11.6.44 Find the Equation for a Surface
The set for all points equidistant from the point (0,0,4) and the \(xy\)-plane.
Solution
Find the distance from the point \(x=y\) and \(z=0\) to the point (0,0,4).
- \( d=\sqrt{x^{2}+y^{2}+(z-4)^{2}} \)
The length is the line from \((x,y,z)\) to the \(xy\)-plane is \( |z| \) so
\( |z| \) | \(= \sqrt{x^{2}+y^{2}+(z-4)^{2}} \) |
\(= x^{2}+y^{2}+z^{2}-8z+16 \) | |
\( 0 \) | \(= x^{2}+y^{2}-8z+16 \) |
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Parent Article: Calculus III Advanced (Course)