 12.4.1E: Find T, N, and for the plane curves in Exercises 1– 4.
 12.4.2E: Find T, N, and for the plane curves in Exercises 1– 4.
 12.4.3E: Find T, N, and for the plane curves in Exercises 1– 4.
 12.4.4E: Find T, N, and for the plane curves in Exercises 1– 4.
 12.4.5E: A formula for the curvature of the graph of a function in the xy p...
 12.4.6E: A formula for the curvature of a parametrized plane curvea. Show th...
 12.4.7E: Normals to plane curvesa. Show that and are both normal to the curv...
 12.4.8E: (Continuation of Exercise 7. )a. Use the method of Exercise 7 to fi...
 12.4.9E: Find T, N, and for the space curves in Exercises 9–16.
 12.4.10E: Find T, N, and for the space curves in Exercises 9–16.
 12.4.11E: Find T, N, and for the space curves in Exercises 9–16.
 12.4.12E: Find T, N, and for the space curves in Exercises 9–16.
 12.4.13E: Find T, N, and for the space curves in Exercises 9–16.
 12.4.14E: Find T, N, and for the space curves in Exercises 9–16.
 12.4.15E: Find T, N, and for the space curves in Exercises 9–16.
 12.4.16E: Find T, N, and for the space curves in Exercises 9–16.
 12.4.17E: Show that the parabola has its largest curvature at its vertex and ...
 12.4.18E: Show that the ellipse x = a cos t, y = b sin t, a > 0, has its larg...
 12.4.19E: Maximizing the curvature of a helix In Example 5, we found the curv...
 12.4.20E: Total curvature We find the total curvature of the portion of a smo...
 12.4.21E: Find an equation for the circle of curvature of the curve at the po...
 12.4.22E: Find an equation for the circle of curvature of the curve at the po...
 12.4.23E: The formula derived in Exercise 5, expresses the curvature k(x) of ...
 12.4.24E: The formula derived in Exercise 5, expresses the curvature k(x) of ...
 12.4.25E: The formula derived in Exercise 5, expresses the curvature k(x) of ...
 12.4.26E: The formula derived in Exercise 5, expresses the curvature k(x) of ...
 12.4.27CE: In Exercises 27–34 you will use a CAS to explore the osculating cir...
 12.4.28CE: In Exercises 27–34 you will use a CAS to explore the osculating cir...
 12.4.29CE: In Exercises 27–34 you will use a CAS to explore the osculating cir...
 12.4.30CE: In Exercises 27–34 you will use a CAS to explore the osculating cir...
 12.4.31CE: In Exercises 27–34 you will use a CAS to explore the osculating cir...
 12.4.32CE: In Exercises 27–34 you will use a CAS to explore the osculating cir...
 12.4.33CE: In Exercises 27–34 you will use a CAS to explore the osculating cir...
 12.4.34CE: In Exercises 27–34 you will use a CAS to explore the osculating cir...
Solutions for Chapter 12.4: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321717399
Solutions for Chapter 12.4
Get Full SolutionsSince 34 problems in chapter 12.4 have been answered, more than 54602 students have viewed full stepbystep solutions from this chapter. University Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321717399. Chapter 12.4 includes 34 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: University Calculus: Early Transcendentals , edition: 2.

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

Completing the square
A method of adding a constant to an expression in order to form a perfect square

Complex conjugates
Complex numbers a + bi and a  bi

Compounded monthly
See Compounded k times per year.

Cycloid
The graph of the parametric equations

Difference identity
An identity involving a trigonometric function of u  v

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

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

Identity matrix
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

Inductive step
See Mathematical induction.

Limaçon
A graph of a polar equation r = a b sin u or r = a b cos u with a > 0 b > 0

Magnitude of a real number
See Absolute value of a real number

Major axis
The line segment through the foci of an ellipse with endpoints on the ellipse

Origin
The number zero on a number line, or the point where the x and yaxes cross in the Cartesian coordinate system, or the point where the x, y, and zaxes cross in Cartesian threedimensional space

Parametric equations for a line in space
The line through P0(x 0, y0, z 0) in the direction of the nonzero vector v = <a, b, c> has parametric equations x = x 0 + at, y = y 0 + bt, z = z0 + ct.

Polynomial function
A function in which ƒ(x)is a polynomial in x, p. 158.

Probability of an event in a finite sample space of equally likely outcomes
The number of outcomes in the event divided by the number of outcomes in the sample space.

Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

Weights
See Weighted mean.

Zoom out
A procedure of a graphing utility used to view more of the coordinate plane (used, for example, to find theend behavior of a function).