 12.7.12E: Tangent planes for F(x, y, z) = 0 Find an equation of the plane tan...
 12.7.31E: Changes in torus surface area The surface area of a torus with an i...
 12.7.45E: Tangent planes Find an equation of the plane tangent to the followi...
 12.7.28E: Approximate function change Use differentials to approximate the ch...
 12.7.27E: Approximate function change Use differentials to approximate the ch...
 12.7.6E: Explain how to approximate the change in a function f when the inde...
 12.7.16E: Tangent planes for z= f (x, y) Find an equation of the plane tangen...
 12.7.17E: Tangent planes for z= f (x, y) Find an equation of the plane tangen...
 12.7.18E: Tangent planes for z= f (x, y) Find an equation of the plane tangen...
 12.7.34E: Volume of a paraboloid The volume of a segment of a circular parabo...
 12.7.35E: Differentials with more than two variables Write the differential ...
 12.7.36E: Differentials with more than two variables Write the differential ...
 12.7.40E: Travel cost The cost of a trip that is L miles long, driving a car ...
 12.7.41E: Explain why or why not Determine whether the following statements ...
 12.7.42E: Tangent planes Find an equation of the plane tangent to the followi...
 12.7.19E: Tangent planes for z= f (x, y) Find an equation of the plane tangen...
 12.7.50E: Heron’s formula The area of a triangle with sides of length a, b, a...
 12.7.51E: Surface area of a cone A cone with height h and radius r has a late...
 12.7.52E: Line tangent to an intersection curve Consider the paraboloid z = x...
 12.7.53E: Batting averages Batting averages in baseball are defined by A = x/...
 12.7.54E: Waterlevel changes A conical tank with radius 0.50 m and height 2....
 12.7.58E: Two electrical resistors When two electrical resistors with resist...
 12.7.59E: Three electrical resistors Extending Exercise 62, when three electr...
 12.7.60AE: Power functions and percent change Suppose that z = f(x, y) = xayb,...
 12.7.61AE: Logarithmic differentials Let f be a differentiable function of one...
 12.7.3E: Write an equation for the plane tangent to the surface f(x, y, z) =...
 12.7.38E: Differentials with more than two variables Write the differential ...
 12.7.25E: Linear approximationa. Find the linear approximation to the functio...
 12.7.46E: Horizontal tangent planes Find the points at which the following s...
 12.7.55E: Flow in a cylinder Poiseuille’s Law is a fundamental law of fluid d...
 12.7.47E: Horizontal tangent planes Find the points at which the following s...
 12.7.33E: Area of an ellipse The area of an ellipse with axes of length 2a an...
 12.7.30E: Approximate function change Use differentials to approximate the ch...
 12.7.22E: Linear approximationa. Find the linear approximation to the functio...
 12.7.39E: Law of Cosines The side lengths of any triangle are related by the ...
 12.7.48E: Horizontal tangent planes Find the points at which the following s...
 12.7.21E: Linear approximationa. Find the linear approximation to the functio...
 12.7.15E: Tangent planes for z= f (x, y) Find an equation of the plane tangen...
 12.7.7E: Write the approximate change formula for a function z = f(x, y)at t...
 12.7.32E: Changes in cone volume The volume of a right circular cone with rad...
 12.7.1E: Suppose n is a vector normal to the tangent plane of the surface f(...
 12.7.20E: Tangent planes for z= f (x, y) Find an equation of the plane tangen...
 12.7.2E: Write the explicit function z = xy2 + x 2y ? 10 in the implicit for...
 12.7.8E: Write the differential dw for the function w = f(x, y, z).
 12.7.37E: Differentials with more than two variables Write the differential ...
 12.7.13E: Tangent planes for F(x, y, z) = 0 Find an equation of the plane tan...
 12.7.29E: Approximate function change Use differentials to approximate the ch...
 12.7.10E: Tangent planes for F(x, y, z) = 0 Find an equation of the plane tan...
 12.7.26E: Linear approximationa. Find the linear approximation to the functio...
 12.7.56E: Floatingpoint operations In general, real numbers (with infinite d...
 12.7.43E: Tangent planes Find an equation of the plane tangent to the followi...
 12.7.9E: Tangent planes for F(x, y, z) = 0 Find an equation of the plane tan...
 12.7.4E: Write an equation for the plane tangent to the surface z = f(x, y) ...
 12.7.14E: Tangent planes for F(x, y, z) = 0 Find an equation of the plane tan...
 12.7.24E: Linear approximationa. Find the linear approximation to the functio...
 12.7.49E: Horizontal tangent planes Find the points at which the following s...
 12.7.57E: Probability of at least one encounter Suppose that in a large group...
 12.7.44E: Tangent planes Find an equation of the plane tangent to the followi...
 12.7.11E: Tangent planes for F(x, y, z) = 0 Find an equation of the plane tan...
 12.7.62AE: Distance from a plane to an ellipsoid (Adapted from 1938 Putnam Ex...
 12.7.5E: Explain how to approximate a function f at a point near (a, b)where...
 12.7.23E: Linear approximationa. Find the linear approximation to the functio...
Solutions for Chapter 12.7: Calculus: Early Transcendentals 1st Edition
Full solutions for Calculus: Early Transcendentals  1st Edition
ISBN: 9780321570567
Solutions for Chapter 12.7
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This 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 12.7 includes 62 full stepbystep solutions. Since 62 problems in chapter 12.7 have been answered, more than 150581 students have viewed full stepbystep solutions from this chapter.

Acute angle
An angle whose measure is between 0° and 90°

Bias
A flaw in the design of a sampling process that systematically causes the sample to differ from the population with respect to the statistic being measured. Undercoverage bias results when the sample systematically excludes one or more segments of the population. Voluntary response bias results when a sample consists only of those who volunteer their responses. Response bias results when the sampling design intentionally or unintentionally influences the responses

Composition of functions
(f ? g) (x) = f (g(x))

Dependent variable
Variable representing the range value of a function (usually y)

Division
a b = aa 1 b b, b Z 0

Factor
In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .

Gaussian curve
See Normal curve.

Intercept
Point where a curve crosses the x, y, or zaxis in a graph.

Law of cosines
a2 = b2 + c2  2bc cos A, b2 = a2 + c2  2ac cos B, c2 = a2 + b2  2ab cos C

Linear correlation
A scatter plot with points clustered along a line. Correlation is positive if the slope is positive and negative if the slope is negative

Newton’s law of cooling
T1t2 = Tm + 1T0  Tm2ekt

Normal curve
The graph of ƒ(x) = ex2/2

Number line graph of a linear inequality
The graph of the solutions of a linear inequality (in x) on a number line

Ordered set
A set is ordered if it is possible to compare any two elements and say that one element is “less than” or “greater than” the other.

Rational zeros
Zeros of a function that are rational numbers.

Real number line
A horizontal line that represents the set of real numbers.

Reflection through the origin
x, y and (x,y) are reflections of each other through the origin.

Sum of complex numbers
(a + bi) + (c + di) = (a + c) + (b + d)i

Terms of a sequence
The range elements of a sequence.

Zero matrix
A matrix consisting entirely of zeros.