 16.6.1: Identify the surface with the given vector equation.
 16.6.2: Identify the surface with the given vector equation.
 16.6.3: Identify the surface with the given vector equation.
 16.6.4: Identify the surface with the given vector equation.
 16.6.5: Use a computer to graph the parametric surface. Get a printout and ...
 16.6.6: Use a computer to graph the parametric surface. Get a printout and ...
 16.6.7: Use a computer to graph the parametric surface. Get a printout and ...
 16.6.8: Use a computer to graph the parametric surface. Get a printout and ...
 16.6.9: Use a computer to graph the parametric surface. Get a printout and ...
 16.6.10: Use a computer to graph the parametric surface. Get a printout and ...
 16.6.11: Match the equations with the graphs labeled IVI and give reasons fo...
 16.6.12: Match the equations with the graphs labeled IVI and give reasons fo...
 16.6.13: Match the equations with the graphs labeled IVI and give reasons fo...
 16.6.14: Match the equations with the graphs labeled IVI and give reasons fo...
 16.6.15: Match the equations with the graphs labeled IVI and give reasons fo...
 16.6.16: Match the equations with the graphs labeled IVI and give reasons fo...
 16.6.17: Find a parametric representation for the surface.
 16.6.18: Find a parametric representation for the surface.
 16.6.19: Find a parametric representation for the surface.
 16.6.20: Find a parametric representation for the surface.
 16.6.21: Find a parametric representation for the surface.
 16.6.22: Find a parametric representation for the surface.
 16.6.23: Find a parametric representation for the surface.
 16.6.24: Find a parametric representation for the surface.
 16.6.25: Use a computer algebra system to produce a graph that looks like th...
 16.6.26: Use a computer algebra system to produce a graph that looks like th...
 16.6.27: Find parametric equations for the surface obtained by rotating the ...
 16.6.28: Find parametric equations for the surface obtained by rotating the ...
 16.6.29: (a) What happens to the spiral tube in Example 2 (see Figure 5) if ...
 16.6.30: The surface with parametric equations where and , is called a Mbius...
 16.6.31: Find an equation of the tangent plane to the given parametric surfa...
 16.6.32: Find an equation of the tangent plane to the given parametric surfa...
 16.6.33: Find an equation of the tangent plane to the given parametric surfa...
 16.6.34: Find an equation of the tangent plane to the given parametric surfa...
 16.6.35: Find the area of the surface.
 16.6.36: Find the area of the surface.
 16.6.37: Find the area of the surface.
 16.6.38: Find the area of the surface.
 16.6.39: Find the area of the surface.
 16.6.40: Find the area of the surface.
 16.6.41: Find the area of the surface.
 16.6.42: Find the area of the surface.
 16.6.43: Find the area of the surface.
 16.6.44: Find the area of the surface.
 16.6.45: Find the area of the surface.
 16.6.46: Find the area of the surface correct to four decimal places by expr...
 16.6.47: Find the area of the surface correct to four decimal places by expr...
 16.6.48: Find, to four decimal places, the area of the part of the surface t...
 16.6.49: (a) Use the Midpoint Rule for double integrals (see Section 15.1) w...
 16.6.50: Find the area of the surface with vector equation , , . State your ...
 16.6.51: Find the exact area of the surface , , .
 16.6.52: (a) Set up, but do not evaluate, a double integral for the area of ...
 16.6.53: (a) Show that the parametric equations , , ,, , represent an ellips...
 16.6.54: (a) Show that the parametric equations , , , represent a hyperboloi...
 16.6.55: Find the area of the surface in Exercise 7 correct to four decimal ...
 16.6.56: (a) Find a parametric representation for the torus obtained by rota...
Solutions for Chapter 16.6: Parametric Surfaces and Their Areas
Full solutions for Calculus,  5th Edition
ISBN: 9780534393397
Solutions for Chapter 16.6: Parametric Surfaces and Their Areas
Get Full SolutionsCalculus, was written by and is associated to the ISBN: 9780534393397. This textbook survival guide was created for the textbook: Calculus,, edition: 5. Chapter 16.6: Parametric Surfaces and Their Areas includes 56 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 56 problems in chapter 16.6: Parametric Surfaces and Their Areas have been answered, more than 43547 students have viewed full stepbystep solutions from this chapter.

Basic logistic function
The function ƒ(x) = 1 / 1 + ex

Cycloid
The graph of the parametric equations

Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)

Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x )  x 2)2 + (y1  y2)2 + (z 1  z 2)2

Equal complex numbers
Complex numbers whose real parts are equal and whose imaginary parts are equal.

First octant
The points (x, y, z) in space with x > 0 y > 0, and z > 0.

Frequency
Reciprocal of the period of a sinusoid.

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

Positive angle
Angle generated by a counterclockwise rotation.

Power rule of logarithms
logb Rc = c logb R, R 7 0.

Reflection through the origin
x, y and (x,y) are reflections of each other through the origin.

Reflexive property of equality
a = a

Regression model
An equation found by regression and which can be used to predict unknown values.

Secant line of ƒ
A line joining two points of the graph of ƒ.

Second quartile
See Quartile.

Sphere
A set of points in Cartesian space equally distant from a fixed point called the center.

Standard form of a complex number
a + bi, where a and b are real numbers

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Upper bound test for real zeros
A test for finding an upper bound for the real zeros of a polynomial.

Work
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.