 12.1.48E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.70E: ?Solution 70EIdentifying surfaces Identify and briefly describe the...
 12.1.71E: Identifying surfaces Identify and briefly describe the surfaces def...
 12.1.38E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.28E: Parallel planes Find an equation of the plane parallel to the plane...
 12.1.14E: Equations of planes Find an equation of the plane that passes throu...
 12.1.43E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.50E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.68E: Identifying surfaces Identify and briefly describe the surfaces def...
 12.1.85AE: Tilted ellipse Consider the curve r(t) = ?cos t, sin t, c sin t? fo...
 12.1.25E: Parallel planes Find an equation of the plane parallel to the plane...
 12.1.15E: Equations of planes Find an equation of the following planes.The pl...
 12.1.4E: Give an equation of the plane with a normal vector n = ?1, 1, 1? th...
 12.1.33E: Cylinders in ?3 Consider the following cylinders in ?3.a. Identify ...
 12.1.37E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.35E: Cylinders in ?3 Consider the following cylinders in ?3.a. Identify ...
 12.1.6E: Describe the graph of x = z2 in ?3.
 12.1.5E: To which coordinate axes are the following cylinders in ?3 parallel...
 12.1.57E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.29E: Intersecting planes Find an equation of the line of intersection o...
 12.1.42E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.16E: Equations of planes Find an equation of the following planes.The pl...
 12.1.49E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.13E: Equations of planes Find an equation of the plane that passes throu...
 12.1.60E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.78E: Intercepts Let a, b, c, and d be constants. Find the points at whic...
 12.1.23E: Equations of planes For the following sets of planes, determine whi...
 12.1.30E: Intersecting planes Find an equation of the line of intersection o...
 12.1.86AE: Distance from a point to a planea. Show that the point in the plane...
 12.1.9E: What is the name of the surface defined by the equation ?
 12.1.3E: Where does the plane ? 2x ? 3y + 4z = 12 intersect the coordinate a...
 12.1.22E: Properties of planes Find the points at which the following planes ...
 12.1.34E: Cylinders in ?3 Consider the following cylinders in ?3.a. Identify ...
 12.1.62E: Plane containing a line and a point Find an equation of the plane t...
 12.1.2E: Find a vector normal to the plane ?2x ? 3y + 4z = 12.
 12.1.79E: Angle between planes The angle between two planes is the angle ? be...
 12.1.12E: Equations of planes Find an equation of the plane that passes throu...
 12.1.58E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.32E: Intersecting planes Find an equation of the line of intersection o...
 12.1.26E: Parallel planes Find an equation of the plane parallel to the plane...
 12.1.8E: What is the name of the surface defined by the equation ?
 12.1.39E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.1E: Give two pieces of information which, taken together, uniquely dete...
 12.1.7E: What is a trace of a surface?
 12.1.36E: Cylinders in ?3 Consider the following cylinders in ?3.a. Identify ...
 12.1.73E: Identifying surfaces Identify and briefly describe the surfaces def...
 12.1.41E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.19E: Properties of planes Find the points at which the following planes ...
 12.1.24E: Equations of planes For the following sets of planes, determine whi...
 12.1.69E: Identifying surfaces Identify and briefly describe the surfaces def...
 12.1.46E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.64E: Identifying surfaces Identify and briefly describe the surfaces def...
 12.1.65E: Identifying surfaces Identify and briefly describe the surfaces def...
 12.1.66E: Identifying surfaces Identify and briefly describe the surfaces def...
 12.1.72E: Identifying surfaces Identify and briefly describe the surfaces def...
 12.1.80E: Solids of revolution Consider the ellipse x2 + 4y2 = 1 in the xypl...
 12.1.81E: Solids of revolution Which of the quadric surfaces in Table 12.1 ca...
 12.1.82E: Light cones The idea of a light cone appears in the Special Theory ...
 12.1.83E: Tshirt profits A clothing company makes a profit of $10 on its lon...
 12.1.67E: Identifying surfaces Identify and briefly describe the surfaces def...
 12.1.84AE: Parallel line and plane Show that the plane ax + by + cz = d and th...
 12.1.88AE: Ellipsoidplane intersection Let E be the ellipsoidx2/9 + y2/4 + z2...
 12.1.11E: Equations of planes Find an equation of the plane that passes throu...
 12.1.56E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.55E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.47E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.45E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.87AE: Projections Find the projection of the position vector ?2, 3, ?4? o...
 12.1.54E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.40E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.52E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.74E: Curveplane intersections Find the points (if they exist) at which ...
 12.1.44E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.59E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.61E: Explain why or why not Determine whether the following statements a...
 12.1.10E: What is the name of the surface defined by the equation ?
 12.1.21E: Properties of planes Find the points at which the following planes ...
 12.1.17E: Equations of planes Find an equation of the following planes.The pl...
 12.1.18E: Equations of planes Find an equation of the following planes.The pl...
 12.1.51E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.75E: Curveplane intersections Find the points (if they exist) at which ...
 12.1.27E: Parallel planes Find an equation of the plane parallel to the plane...
 12.1.76E: Curveplane intersections Find the points (if they exist) at which ...
 12.1.77E: Curveplane intersections Find the points (if they exist) at which ...
 12.1.53E: Quadric surfaces Consider the following equations of quadric surfac...
 12.1.20E: Properties of planes Find the points at which the following planes ...
 12.1.31E: Intersecting planes Find an equation of the line of intersection o...
 12.1.63E: Matching graphs with equations Match equations af with surfaces A...
Solutions for Chapter 12.1: Calculus: Early Transcendentals 1st Edition
Full solutions for Calculus: Early Transcendentals  1st Edition
ISBN: 9780321570567
Solutions for Chapter 12.1
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 12.1 includes 88 full stepbystep solutions. Since 88 problems in chapter 12.1 have been answered, more than 134708 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

Absolute minimum
A value ƒ(c) is an absolute minimum value of ƒ if ƒ(c) ? ƒ(x)for all x in the domain of ƒ.

Addition property of inequality
If u < v , then u + w < v + w

Arcsine function
See Inverse sine function.

Central angle
An angle whose vertex is the center of a circle

Conic section (or conic)
A curve obtained by intersecting a doublenapped right circular cone with a plane

Event
A subset of a sample space.

Geometric series
A series whose terms form a geometric sequence.

Histogram
A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

Horizontal translation
A shift of a graph to the left or right.

Index of summation
See Summation notation.

Initial point
See Arrow.

Instantaneous rate of change
See Derivative at x = a.

Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

Natural logarithm
A logarithm with base e.

Numerical model
A model determined by analyzing numbers or data in order to gain insight into a phenomenon, p. 64.

Oddeven identity
For a basic trigonometric function f, an identity relating f(x) to f(x).

Order of magnitude (of n)
log n.

Parabola
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Reflection across the xaxis
x, y and (x,y) are reflections of each other across the xaxis.

yzplane
The points (0, y, z) in Cartesian space.