 7.3.33E: Evaluate the following integrals.
 7.3.64E: Using the integral of see3 u By reduction formula 4 in Section 7.2....
 7.3.35E: Evaluate the following integrals.
 7.3.29E: Evaluate the following integrals.
 7.3.36E: Evaluate the following integrals. , x > 10
 7.3.53E: Completing the square Evaluate the following integrals.
 7.3.59E: Area and volume Consider the function f(x) = (9 + x2)–1/2 and the r...
 7.3.67E: Asymmetric integrands Evaluate the following integrals. Consider co...
 7.3.71E: Electric field due to a line of charge A total charge of Q is distr...
 7.3.55E: Completing the square Evaluate the following integrals.
 7.3.79AE: Visual Proof Let . The figure shows that F(x) = area of sector OAB ...
 7.3.49E: Completing the square Evaluate the following integrals.
 7.3.38E: Evaluate the following integrals. , x > 1
 7.3.77AE: Care with the secant substitution Recall that the substitution x = ...
 7.3.48E: Completing the square Evaluate the following integrals.
 7.3.37E: Evaluate the following integrals.
 7.3.60E: Area of a region Graph the function f(x) = (16 + x2)–3/2 and find t...
 7.3.22E: Evaluate the following integrals. , x > 6
 7.3.31E: Evaluate the following integrals.
 7.3.41E: Evaluating definite integrals Evaluate the following definite integ...
 7.3.76AE: Care with the secant substitution Recall that the substitution x = ...
 7.3.57E: Area of a segment of a circle Use two approaches to show that the a...
 7.3.72E: Magnetic field due to current in a straight wire A long straight wi...
 7.3.78AE: Care with the secant substitution Recall that the substitution x = ...
 7.3.74E: Maximum path length of a projectile (Adapted from Putnam Exam 1940)...
 7.3.28E: Evaluate the following integrals.
 7.3.73E: Fastest descent time The cycloid is the curve traced by a point on ...
 7.3.20E: Evaluate the following integrals.
 7.3.69E: A torus (doughnut) Find the volume of the solid torus formed when t...
 7.3.52E: Completing the square Evaluate the following integrals. , x > 4
 7.3.32E: Evaluate the following integrals.
 7.3.42E: Evaluating definite integrals Evaluate the following definite integ...
 7.3.21E: Evaluate the following integrals.
 7.3.68E: Clever substitution Evaluate using the substitution x = 2 tan–1 ?. ...
 7.3.25E: Evaluate the following integrals. , x >3
 7.3.51E: Completing the square Evaluate the following integrals.
 7.3.24E: Evaluate the following integrals.
 7.3.63E: Using the integral of sec3 u By reduction formula 4 in Section 7.2....
 7.3.34E: Evaluate the following integrals.
 7.3.43E: Evaluating definite integrals Evaluate the following definite integ...
 7.3.54E: Completing the square Evaluate the following integrals.
 7.3.19E: Evaluate the following integrals. , x > 9
 7.3.50E: Completing the square Evaluate the following integrals.
 7.3.65E: Using the integral of see3 u By reduction formula 4 in Section 7.2....
 7.3.40E: Evaluate the following integrals. , x<?
 7.3.47E: Explain why or why not Determine whether the following statements a...
 7.3.23E: Evaluate the following integrals.
 7.3.75AE: Care with the secant substitution Recall that the substitution x = ...
 7.3.30E: Evaluate the following integrals.
 7.3.45E: Evaluating definite integrals Evaluate the following definite integ...
 7.3.58E: Area of a lune A lune is a crescentshaped region bounded by the ar...
 7.3.39E: Evaluate the following integrals. , x > 1
 7.3.26E: Evaluate the following integrals.
 7.3.27E: Evaluate the following integrals.
 7.3.70E: Bagel wars Bob and Bruce bake bagels (shaped like tori). They both ...
 7.3.62E: Comparing areas On the interval [0, 2], the graphs of f(x) = x2/3 a...
 7.3.61E: Arc length of a parabola Find the length of the curve y = ax2 from ...
 7.3.46E: Evaluating definite integrals Evaluate the following definite integ...
 7.3.66E: Asymmetric integrands Evaluate the following integrals. Consider co...
 7.3.56E: Area of an ellipse The upper half of the ellipse centered at the or...
 7.3.44E: Evaluating definite integrals Evaluate the following definite integ...
 7.3.1E: ?What change of variables is suggested by an integral containing \(...
 7.3.2E: ?What change of variables is suggested by an integral containing \(...
 7.3.3E: ?What change of variables is suggested by an integral containing \(...
 7.3.4E: ?If \(x=4 \tan \theta\), express \(\sin \theta\) in terms of x.
 7.3.5E: ?If \(x=2 \sin \theta\), express \(\cot \theta\) in terms of x.
 7.3.6E: ?If \(x=8 \sec \theta\), express \(\tan \theta\) in terms of x.
 7.3.7E: ?Evaluate the following integrals.\(\int_{0}^{5 / 2} \frac{d x}{\sq...
 7.3.8E: Evaluate the following integrals.
 7.3.9E: Evaluate the following integrals.
 7.3.10E: Evaluate the following integrals.
 7.3.11E: ?Evaluate the following integrals.\(\int \frac{d x}{\left(16x^{2}\...
 7.3.12E: Evaluate the following integrals.
 7.3.13E: ?Evaluate the following integrals.
 7.3.14E: Evaluate the following integrals.
 7.3.15E: Evaluate the following integrals.
 7.3.16E: Evaluate the following integrals.
 7.3.17E: Evaluate the following integrals.
 7.3.18E: Evaluate the following integrals.
Solutions for Chapter 7.3: Linear Approximation and Differentials
Full solutions for Calculus: Early Transcendentals  1st Edition
ISBN: 9780321570567
Solutions for Chapter 7.3: Linear Approximation and Differentials
Get Full SolutionsSummary of Chapter 7.3: Linear Approximation and Differentials
The theme of this section is optimization, a topic arising in many disciplines that rely on mathematics.
This expansive textbook survival guide covers the following chapters and their solutions. Chapter 7.3: Linear Approximation and Differentials includes 79 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since 79 problems in chapter 7.3: Linear Approximation and Differentials have been answered, more than 410986 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

Additive inverse of a complex number
The opposite of a + bi, or a  bi

Angle
Union of two rays with a common endpoint (the vertex). The beginning ray (the initial side) can be rotated about its endpoint to obtain the final position (the terminal side)

Boundary
The set of points on the “edge” of a region

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

Convergence of a series
A series aqk=1 ak converges to a sum S if imn: q ank=1ak = S

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Equivalent arrows
Arrows that have the same magnitude and direction.

Equivalent systems of equations
Systems of equations that have the same solution.

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

Focus, foci
See Ellipse, Hyperbola, Parabola.

Hypotenuse
Side opposite the right angle in a right triangle.

Inequality
A statement that compares two quantities using an inequality symbol

Instantaneous rate of change
See Derivative at x = a.

Limit
limx:aƒ1x2 = L means that ƒ(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a

Mean (of a set of data)
The sum of all the data divided by the total number of items

Nappe
See Right circular cone.

Randomization
The principle of experimental design that makes it possible to use the laws of probability when making inferences.

Secant line of ƒ
A line joining two points of the graph of ƒ.

Weighted mean
A mean calculated in such a way that some elements of the data set have higher weights (that is, are counted more strongly in determining the mean) than others.

xzplane
The points x, 0, z in Cartesian space.