 13.7.1: In Exercises 14, describe the level surface
 13.7.2: In Exercises 14, describe the level surface
 13.7.3: In Exercises 14, describe the level surface
 13.7.4: In Exercises 14, describe the level surface
 13.7.5: In Exercises 514, find a unit normal vector to the surface at the g...
 13.7.6: In Exercises 514, find a unit normal vector to the surface at the g...
 13.7.7: In Exercises 514, find a unit normal vector to the surface at the g...
 13.7.8: In Exercises 514, find a unit normal vector to the surface at the g...
 13.7.9: In Exercises 514, find a unit normal vector to the surface at the g...
 13.7.10: In Exercises 514, find a unit normal vector to the surface at the g...
 13.7.11: In Exercises 514, find a unit normal vector to the surface at the g...
 13.7.12: In Exercises 514, find a unit normal vector to the surface at the g...
 13.7.13: In Exercises 514, find a unit normal vector to the surface at the g...
 13.7.14: In Exercises 514, find a unit normal vector to the surface at the g...
 13.7.15: In Exercises 1518, find an equation of the tangent plane to the sur...
 13.7.16: In Exercises 1518, find an equation of the tangent plane to the sur...
 13.7.17: In Exercises 1518, find an equation of the tangent plane to the sur...
 13.7.18: In Exercises 1518, find an equation of the tangent plane to the sur...
 13.7.19: In Exercises 1928, find an equation of the tangent plane to the sur...
 13.7.20: In Exercises 1928, find an equation of the tangent plane to the sur...
 13.7.21: In Exercises 1928, find an equation of the tangent plane to the sur...
 13.7.22: In Exercises 1928, find an equation of the tangent plane to the sur...
 13.7.23: In Exercises 1928, find an equation of the tangent plane to the sur...
 13.7.24: In Exercises 1928, find an equation of the tangent plane to the sur...
 13.7.25: In Exercises 1928, find an equation of the tangent plane to the sur...
 13.7.26: In Exercises 1928, find an equation of the tangent plane to the sur...
 13.7.27: In Exercises 1928, find an equation of the tangent plane to the sur...
 13.7.28: In Exercises 1928, find an equation of the tangent plane to the sur...
 13.7.29: In Exercises 2934, find an equation of the tangent plane and find s...
 13.7.30: In Exercises 2934, find an equation of the tangent plane and find s...
 13.7.31: In Exercises 2934, find an equation of the tangent plane and find s...
 13.7.32: In Exercises 2934, find an equation of the tangent plane and find s...
 13.7.33: In Exercises 2934, find an equation of the tangent plane and find s...
 13.7.34: In Exercises 2934, find an equation of the tangent plane and find s...
 13.7.35: Investigation Consider the function on the intervals and (a) Find a...
 13.7.36: Investigation Consider the function on the intervals and (a) Find a...
 13.7.37: Consider the function which is differentiable at Give the definitio...
 13.7.38: Give the standard form of the equation of the tangent plane to a su...
 13.7.39: For some surfaces, the normal lines at any point pass through the s...
 13.7.40: For some surfaces, the normal lines at any point pass through the s...
 13.7.41: In Exercises 41 46, (a) find symmetric equations of the tangent lin...
 13.7.42: In Exercises 41 46, (a) find symmetric equations of the tangent lin...
 13.7.43: In Exercises 41 46, (a) find symmetric equations of the tangent lin...
 13.7.44: In Exercises 41 46, (a) find symmetric equations of the tangent lin...
 13.7.45: In Exercises 41 46, (a) find symmetric equations of the tangent lin...
 13.7.46: In Exercises 41 46, (a) find symmetric equations of the tangent lin...
 13.7.47: Consider the functions and (a) Find a set of parametric equations o...
 13.7.48: Consider the functions and (a) Use a computer algebra system to gra...
 13.7.49: In Exercises 4952, find the angle of inclination of the tangent pla...
 13.7.50: In Exercises 4952, find the angle of inclination of the tangent pla...
 13.7.51: In Exercises 4952, find the angle of inclination of the tangent pla...
 13.7.52: In Exercises 4952, find the angle of inclination of the tangent pla...
 13.7.53: In Exercises 53 and 54, find the point on the surface where the tan...
 13.7.54: In Exercises 53 and 54, find the point on the surface where the tan...
 13.7.55: HeatSeeking Path In Exercises 55 and 56, find the path of a heats...
 13.7.56: HeatSeeking Path In Exercises 55 and 56, find the path of a heats...
 13.7.57: In Exercises 57 and 58, show that the tangent plane to the quadric ...
 13.7.58: In Exercises 57 and 58, show that the tangent plane to the quadric ...
 13.7.59: Show that any tangent plane to the cone passes through the origin.
 13.7.60: Let be a differentiable function and consider the surface Show that...
 13.7.61: Approximation Consider the following approximations for a function ...
 13.7.62: Approximation Repeat Exercise 61 for the function
 13.7.63: Prove Theorem 13.14.
 13.7.64: Prove that the angle of inclination of the tangent plane to the sur...
Solutions for Chapter 13.7: Tangent Planes and Normal Lines
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 13.7: Tangent Planes and Normal Lines
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Calculus was written by and is associated to the ISBN: 9780618502981. Since 64 problems in chapter 13.7: Tangent Planes and Normal Lines have been answered, more than 78319 students have viewed full stepbystep solutions from this chapter. Chapter 13.7: Tangent Planes and Normal Lines includes 64 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus, edition: 8.

Branches
The two separate curves that make up a hyperbola

Combination
An arrangement of elements of a set, in which order is not important

Conjugate axis of a hyperbola
The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2

Event
A subset of a sample space.

Identity function
The function ƒ(x) = x.

Irrational zeros
Zeros of a function that are irrational numbers.

Law of sines
sin A a = sin B b = sin C c

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

Pythagorean
Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

Quantitative variable
A variable (in statistics) that takes on numerical values for a characteristic being measured.

Range of a function
The set of all output values corresponding to elements in the domain.

Reexpression of data
A transformation of a data set.

Remainder theorem
If a polynomial f(x) is divided by x  c , the remainder is ƒ(c)

Rose curve
A graph of a polar equation or r = a cos nu.

Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt

Slant asymptote
An end behavior asymptote that is a slant line

Vector equation for a line in space
The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.

Vertical component
See Component form of a vector.

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.