 11.5.24E: Curves in space Graph the curves described by the following functio...
 11.5.57AE: Curves on spheresGraph the curve and prove that it lies on the surf...
 11.5.11E: Equations of lines Find an equation of the following lines, Make a ...
 11.5.6E: In what plane does the curve r(t) = ti + t2k lie?
 11.5.49E: Matching functions with graphs Match functions af with the appropr...
 11.5.37E: Explain why or why not Determine whether the following statements a...
 11.5.39E: Domains Find the domain of the following vectorvalued functions.
 11.5.14E: Equations of lines Find equations of the following linesThe line th...
 11.5.35E: Limits Evaluate the following limits
 11.5.17E: Line segments Find an equation of the line segment joining the firs...
 11.5.44E: Lineplane intersections Find the point (if it exists) at which the...
 11.5.2E: How many dependent scalar variables does the function r(t) = ?f(t),...
 11.5.59AE: Curves on spheresFind the period of the function in the Exercise, t...
 11.5.12E: Equations of lines Find an equation of the following lines, Make a ...
 11.5.19E: Line segments Find an equation of the line segment joining the firs...
 11.5.48E: Curveplane intersections Find the points (if they exist) at which ...
 11.5.29E: Exotic curves Graph the curves described by the following functions...
 11.5.47E: Curveplane intersections Find the points (if they exist) at which ...
 11.5.60AE: Limits of vector functions Let r(t) = ?f(t), g(t),h(t)?.a. Assume t...
 11.5.51E: Upward path Consider the curve described by the vector function r(t...
 11.5.40E: Domains Find the domain of the following vectorvalued functions.
 11.5.23E: Curves in space Graph the curves described by the following functio...
 11.5.18E: Line segments Find an equation of the line segment joining the firs...
 11.5.8E: How do you determine whether r(t) = f(t) i, g(t) j, h(t) k is conti...
 11.5.4E: Explain how to find a vector in the direction of the line segment f...
 11.5.56E: Applications of parametric curves are considered in detail in Secti...
 11.5.16E: Equations of lines Find equations of the following linesThe line th...
 11.5.33E: Limits Evaluate the following limits
 11.5.45E: Lineplane intersections Find the point (if it exists) at which the...
 11.5.41E: Domains Find the domain of the following vectorvalued functions.
 11.5.31E: Exotic curves Graph the curves described by the following functions...
 11.5.9E: Equations of lines Find equations of the following linesThe line th...
 11.5.32E: Exotic curves Graph the curves described by the following functions...
 11.5.50E: Intersecting lines and colliding particles Consider the linesr(t) =...
 11.5.52E: Closed plane curves Consider the curve r (t) = (a cos t + b sin t)i...
 11.5.53E: Closed plane curves Consider the curve r (t) = (a cos t + b sin t)i...
 11.5.54E: Closed plane curves Consider the curve r (t) = (a cos t + b sin t)i...
 11.5.22E: Curves in space Graph the curves described by the following functio...
 11.5.43E: Lineplane intersections Find the point (if it exists) at which the...
 11.5.10E: Equations of lines Find equations of the following linesThe line th...
 11.5.55E: Closed plane curves Consider the curve r (t) = (a cos t + b sin t)i...
 11.5.46E: Curveplane intersections Find the points (if they exist) at which ...
 11.5.38E: Domains Find the domain of the following vectorvalued functions.
 11.5.25E: Curves in space Graph the curves described by the following functio...
 11.5.28E: Curves in space Graph the curves described by the following functio...
 11.5.1E: How many independent variables does the function r(t) = ?f(t), g(t)...
 11.5.34E: Limits Evaluate the following limits
 11.5.13E: Equations of lines Find equations of the following linesThe line th...
 11.5.30E: Exotic curves Graph the curves described by the following functions...
 11.5.58AE: Curves on spheresProve that for integers m and n, the curve lies on...
 11.5.42E: Lineplane intersections Find the point (if it exists) at which the...
 11.5.20E: Line segments Find an equation of the line segment joining the firs...
 11.5.26E: Curves in space Graph the curves described by the following functio...
 11.5.3E: Why is r(t) = ?f(t), g(t), h(t)? called a vectorvalued function?
 11.5.21E: Curves in space Graph the curves described by the following functio...
 11.5.15E: Equations of lines Find equations of the following linesThe line th...
 11.5.5E: What is an equation of the line through the points P0(x0, y0, z0) a...
 11.5.7E: How do you evaluate where r(t) = ?f(t), g(t), h(t)??
 11.5.36E: Limits Evaluate the following limits
 11.5.27E: Curves in space Graph the curves described by the following functio...
Solutions for Chapter 11.5: Calculus: Early Transcendentals 1st Edition
Full solutions for Calculus: Early Transcendentals  1st Edition
ISBN: 9780321570567
Solutions for Chapter 11.5
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Chapter 11.5 includes 60 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 60 problems in chapter 11.5 have been answered, more than 140583 students have viewed full stepbystep solutions from this chapter.

Cardioid
A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.

Complex plane
A coordinate plane used to represent the complex numbers. The xaxis of the complex plane is called the real axis and the yaxis is the imaginary axis

Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)

Expanded form
The right side of u(v + w) = uv + uw.

Inverse secant function
The function y = sec1 x

Inverse sine function
The function y = sin1 x

Lemniscate
A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.

Linear function
A function that can be written in the form ƒ(x) = mx + b, where and b are real numbers

Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)

Multiplicative inverse of a complex number
The reciprocal of a + bi, or 1 a + bi = a a2 + b2 ba2 + b2 i

Normal distribution
A distribution of data shaped like the normal curve.

nth root of a complex number z
A complex number v such that vn = z

Phase shift
See Sinusoid.

Second quartile
See Quartile.

Solve a triangle
To find one or more unknown sides or angles of a triangle

Spiral of Archimedes
The graph of the polar curve.

Sum identity
An identity involving a trigonometric function of u + v

xcoordinate
The directed distance from the yaxis yzplane to a point in a plane (space), or the first number in an ordered pair (triple), pp. 12, 629.

zaxis
Usually the third dimension in Cartesian space.