 16.6.1: Determine whether the points and lie on the given surface.
 16.6.2: Determine whether the points and lie on the given surface.
 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: Identify the surface with the given vector equation.
 16.6.6: Identify the surface with the given vector equation.
 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: Use a computer to graph the parametric surface. Get a printout and ...
 16.6.12: Use a computer to graph the parametric surface. Get a printout and ...
 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: Match the equations with the graphs labeled IVI and give reasons fo...
 16.6.18: Match the equations with the graphs labeled IVI and give reasons fo...
 16.6.19: Find a parametric representation for the surface. The plane through...
 16.6.20: Find a parametric representation for the surface. The plane that pa...
 16.6.21: Find a parametric representation for the surface. The part of the h...
 16.6.22: Find a parametric representation for the surface. The part of the e...
 16.6.23: Find a parametric representation for the surface. The part of the s...
 16.6.24: Find a parametric representation for the surface. The part of the s...
 16.6.25: Find a parametric representation for the surface. The part of the c...
 16.6.26: Find a parametric representation for the surface. The part of the p...
 16.6.27: Use a computer algebra system to produce a graph that looks like th...
 16.6.28: Use a computer algebra system to produce a graph that looks like th...
 16.6.29: Find parametric equations for the surface obtained by rotating the ...
 16.6.30: Find parametric equations for the surface obtained by rotating the ...
 16.6.31: (a) What happens to the spiral tube in Example 2 (see Figure 5) if ...
 16.6.32: The surface with parametric equations where and , is called a Mbius...
 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 an equation of the tangent plane to the given parametric surfa...
 16.6.36: Find an equation of the tangent plane to the given parametric surfa...
 16.6.37: Find an equation of the tangent plane to the given parametric surfa...
 16.6.38: Find an equation of the tangent plane to the given parametric surfa...
 16.6.39: Find the area of the surface. The part of the plane that lies in th...
 16.6.40: Find the area of the surface. The part of the plane with vector equ...
 16.6.41: Find the area of the surface. The part of the plane that lies insid...
 16.6.42: Find the area of the surface. The part of the cone that lies betwee...
 16.6.43: Find the area of the surface. The surface , ,
 16.6.44: Find the area of the surface. The part of the surface that lies abo...
 16.6.45: Find the area of the surface. The part of the surface that lies wit...
 16.6.46: Find the area of the surface. The part of the paraboloid that lies ...
 16.6.47: Find the area of the surface. The part of the surface that lies bet...
 16.6.48: Find the area of the surface. The helicoid (or spiral ramp) with ve...
 16.6.49: Find the area of the surface. The surface with parametric equations...
 16.6.50: Find the area of the surface. The part of the sphere that lies insi...
 16.6.51: If the equation of a surface is , where , and you know that and , w...
 16.6.52: Find the area of the surface correct to four decimal places by expr...
 16.6.53: Find the area of the surface correct to four decimal places by expr...
 16.6.54: Find, to four decimal places, the area of the part of the surface t...
 16.6.55: (a) Use the Midpoint Rule for double integrals (see Sec  tion 15.1...
 16.6.56: Find the area of the surface with vector equation , , . State your ...
 16.6.57: Find the exact area of the surface , , .
 16.6.58: (a) Set up, but do not evaluate, a double integral for the area of ...
 16.6.59: (a) Show that the parametric equations , , , , , represent an ellip...
 16.6.60: (a) Show that the parametric equations , , , represent a hyperboloi...
 16.6.61: Find the area of the part of the sphere that lies inside the parabo...
 16.6.62: The figure shows the surface created when the cylinder intersects t...
 16.6.63: Find the area of the part of the sphere that lies inside the cylind...
 16.6.64: (a) Find a parametric representation for the torus obtained by rota...
Solutions for Chapter 16.6: PARAMETRIC SURFACES AND THEIR AREAS
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Solutions for Chapter 16.6: PARAMETRIC SURFACES AND THEIR AREAS
Get Full SolutionsSince 64 problems in chapter 16.6: PARAMETRIC SURFACES AND THEIR AREAS have been answered, more than 23456 students have viewed full stepbystep solutions from this chapter. Multivariable Calculus, was written by and is associated to the ISBN: 9780538497879. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 16.6: PARAMETRIC SURFACES AND THEIR AREAS includes 64 full stepbystep solutions. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7.

Acute angle
An angle whose measure is between 0° and 90°

Additive inverse of a real number
The opposite of b , or b

Correlation coefficient
A measure of the strength of the linear relationship between two variables, pp. 146, 162.

Discriminant
For the equation ax 2 + bx + c, the expression b2  4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2  4AC

DMS measure
The measure of an angle in degrees, minutes, and seconds

Eccentricity
A nonnegative number that specifies how offcenter the focus of a conic is

Focal width of a parabola
The length of the chord through the focus and perpendicular to the axis.

Gaussian elimination
A method of solving a system of n linear equations in n unknowns.

Inverse tangent function
The function y = tan1 x

Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Quadratic equation in x
An equation that can be written in the form ax 2 + bx + c = 01a ? 02

Real zeros
Zeros of a function that are real numbers.

Sine
The function y = sin x.

Standard form of a polynomial function
ƒ(x) = an x n + an1x n1 + Á + a1x + a0

Symmetric matrix
A matrix A = [aij] with the property aij = aji for all i and j

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Venn diagram
A visualization of the relationships among events within a sample space.

Vertical line
x = a.

Viewing window
The rectangular portion of the coordinate plane specified by the dimensions [Xmin, Xmax] by [Ymin, Ymax].