 12.4.1: Finding the Unit Tangent Vector In Exercises 16, find the unit tang...
 12.4.2: Finding the Unit Tangent Vector In Exercises 16, find the unit tang...
 12.4.3: Finding the Unit Tangent Vector In Exercises 16, find the unit tang...
 12.4.4: Finding the Unit Tangent Vector In Exercises 16, find the unit tang...
 12.4.5: Finding the Unit Tangent Vector In Exercises 16, find the unit tang...
 12.4.6: Finding the Unit Tangent Vector In Exercises 16, find the unit tang...
 12.4.7: Finding a Tangent Line In Exercises 712, find the unit tangent vect...
 12.4.8: Finding a Tangent Line In Exercises 712, find the unit tangent vect...
 12.4.9: Finding a Tangent Line In Exercises 712, find the unit tangent vect...
 12.4.10: Finding a Tangent Line In Exercises 712, find the unit tangent vect...
 12.4.11: Finding a Tangent Line In Exercises 712, find the unit tangent vect...
 12.4.12: Finding a Tangent Line In Exercises 712, find the unit tangent vect...
 12.4.13: Finding the Principal Unit Normal Vector In Exercises 1320, find th...
 12.4.14: Finding the Principal Unit Normal Vector In Exercises 1320, find th...
 12.4.15: Finding the Principal Unit Normal Vector In Exercises 1320, find th...
 12.4.16: Finding the Principal Unit Normal Vector In Exercises 1320, find th...
 12.4.17: Finding the Principal Unit Normal Vector In Exercises 1320, find th...
 12.4.18: Finding the Principal Unit Normal Vector In Exercises 1320, find th...
 12.4.19: Finding the Principal Unit Normal Vector In Exercises 1320, find th...
 12.4.20: Finding the Principal Unit Normal Vector In Exercises 1320, find th...
 12.4.21: Finding Tangential and Normal Components of Acceleration In Exercis...
 12.4.22: Finding Tangential and Normal Components of Acceleration In Exercis...
 12.4.23: Finding Tangential and Normal Components of Acceleration In Exercis...
 12.4.24: Finding Tangential and Normal Components of Acceleration In Exercis...
 12.4.25: Finding Tangential and Normal Components of Acceleration In Exercis...
 12.4.26: Finding Tangential and Normal Components of Acceleration In Exercis...
 12.4.27: Finding Tangential and Normal Components of Acceleration In Exercis...
 12.4.28: Finding Tangential and Normal Components of Acceleration In Exercis...
 12.4.29: Circular Motion In Exercises 2932, consider an object moving accord...
 12.4.30: Circular Motion In Exercises 2932, consider an object moving accord...
 12.4.31: Circular Motion In Exercises 2932, consider an object moving accord...
 12.4.32: Circular Motion In Exercises 2932, consider an object moving accord...
 12.4.33: Sketching a Graph and Vectors In Exercises 3336, sketch the graph o...
 12.4.34: Sketching a Graph and Vectors In Exercises 3336, sketch the graph o...
 12.4.35: Sketching a Graph and Vectors In Exercises 3336, sketch the graph o...
 12.4.36: Sketching a Graph and Vectors In Exercises 3336, sketch the graph o...
 12.4.37: Finding Vectors In Exercises 3742, find and at the given time for t...
 12.4.38: Finding Vectors In Exercises 3742, find and at the given time for t...
 12.4.39: Finding Vectors In Exercises 3742, find and at the given time for t...
 12.4.40: Finding Vectors In Exercises 3742, find and at the given time for t...
 12.4.41: Finding Vectors In Exercises 3742, find and at the given time for t...
 12.4.42: Finding Vectors In Exercises 3742, find and at the given time for t...
 12.4.43: Definitions Define the unit tangent vector, the principal unit norm...
 12.4.44: Unit Tangent Vector How is the unit tangent vector related to the o...
 12.4.45: Acceleration Describe the motion of a particle when the normal comp...
 12.4.46: Acceleration Describe the motion of a particle when the tangential ...
 12.4.47: Finding Vectors An object moves along the path given by Find and (i...
 12.4.48: HOW DO YOU SEE IT? The figures show the paths of two particles. (i)...
 12.4.49: Cycloidal Motion The figure shows the path of a particle modeled by...
 12.4.50: Motion Along an Involute of a Circle The figure shows a particle mo...
 12.4.51: Finding a Binormal Vector In Exercises 5156, find the vectors T and...
 12.4.52: Finding a Binormal Vector In Exercises 5156, find the vectors T and...
 12.4.53: Finding a Binormal Vector In Exercises 5156, find the vectors T and...
 12.4.54: Finding a Binormal Vector In Exercises 5156, find the vectors T and...
 12.4.55: Finding a Binormal Vector In Exercises 5156, find the vectors T and...
 12.4.56: Finding a Binormal Vector In Exercises 5156, find the vectors T and...
 12.4.57: Alternative Formula for the Principal Unit Normal Vector In Exercis...
 12.4.58: Alternative Formula for the Principal Unit Normal Vector In Exercis...
 12.4.59: Alternative Formula for the Principal Unit Normal Vector In Exercis...
 12.4.60: Alternative Formula for the Principal Unit Normal Vector In Exercis...
 12.4.61: Projectile Motion Find the tangential and normal components of acce...
 12.4.62: Projectile Motion Use your results from Exercise 61 to find the tan...
 12.4.63: Projectile Motion A projectile is launched with an initial velocity...
 12.4.64: Projectile Motion A projectile is launched with an initial velocity...
 12.4.65: Air Traffic Control Because of a storm, ground controllers instruct...
 12.4.66: Projectile Motion A plane flying at an altitude of 36,000 feet at a...
 12.4.67: Centripetal Acceleration An object is spinning at a constant speed ...
 12.4.68: Centripetal Force An object of mass moves at a constant speed in a ...
 12.4.69: The orbit of the International Space Station 255 miles above the su...
 12.4.70: The orbit of the Hubble telescope 360 miles above the surface of Earth
 12.4.71: The orbit of a heat capacity mapping satellite 385 miles above the ...
 12.4.72: The orbit of a communications satellite miles above the surface of ...
 12.4.73: True or False? In Exercises 73 and 74, determine whether the statem...
 12.4.74: True or False? In Exercises 73 and 74, determine whether the statem...
 12.4.75: Motion of a Particle A particle moves along a path modeled by where...
 12.4.76: Proof Prove that the principal unit normal vector points toward the...
 12.4.77: Proof Prove that the vector is 0 for an object moving in a straight...
 12.4.78: Proof Prove that
 12.4.79: Proof Prove that aN _ __a_2 _ aT 2.
 12.4.80: A particle of unit mass moves on a straight line under the action o...
Solutions for Chapter 12.4: Tangent Vectors and Normal Vectors
Full solutions for Calculus: Early Transcendental Functions  6th Edition
ISBN: 9781285774770
Solutions for Chapter 12.4: Tangent Vectors and Normal Vectors
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9781285774770. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions, edition: 6. Chapter 12.4: Tangent Vectors and Normal Vectors includes 80 full stepbystep solutions. Since 80 problems in chapter 12.4: Tangent Vectors and Normal Vectors have been answered, more than 45545 students have viewed full stepbystep solutions from this chapter.

Absolute value of a vector
See Magnitude of a vector.

Bounded
A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Circular functions
Trigonometric functions when applied to real numbers are circular functions

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

Hypotenuse
Side opposite the right angle in a right triangle.

Multiplicity
The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x  c) (x  z 2) Á (x  z n)

nth root
See Principal nth root

Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Quartic function
A degree 4 polynomial function.

Real axis
See Complex plane.

Reflection
Two points that are symmetric with respect to a lineor a point.

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

Series
A finite or infinite sum of terms.

Slant line
A line that is neither horizontal nor vertical

Spiral of Archimedes
The graph of the polar curve.

Stretch of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal stretch) by the constant 1/c, or all of the ycoordinates (vertical stretch) of the points by a constant c, c, > 1.

Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.

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