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# Solutions for Chapter 2.6: Trigonometric Substitutions ## Full solutions for Calculus: Early Transcendentals | 1st Edition

ISBN: 9780321570567 Solutions for Chapter 2.6: Trigonometric Substitutions

Solutions for Chapter 2.6
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##### ISBN: 9780321570567

Summary of Chapter 2.6: Trigonometric Substitutions

In this section, we introduce a new family of functions called the hyperbolic functions, which are closely related to both trigonometric functions and exponential functions.

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Chapter 2.6: Trigonometric Substitutions includes 7 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 7 problems in chapter 2.6: Trigonometric Substitutions have been answered, more than 411917 students have viewed full step-by-step solutions from this chapter. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567.

Key Calculus Terms and definitions covered in this textbook
• Absolute minimum

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

• Argument of a complex number

The argument of a + bi is the direction angle of the vector {a,b}.

• Binomial

A polynomial with exactly two terms

• Causation

A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable

• Circle

A set of points in a plane equally distant from a fixed point called the center

• Components of a vector

See Component form of a vector.

• Definite integral

The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

• Equilibrium price

See Equilibrium point.

• Horizontal asymptote

The line is a horizontal asymptote of the graph of a function ƒ if lim x:- q ƒ(x) = or lim x: q ƒ(x) = b

• Hyperboloid of revolution

A surface generated by rotating a hyperbola about its transverse axis, p. 607.

• Linear combination of vectors u and v

An expression au + bv , where a and b are real numbers

• Linear equation in x

An equation that can be written in the form ax + b = 0, where a and b are real numbers and a Z 0

• Minor axis

The perpendicular bisector of the major axis of an ellipse with endpoints on the ellipse.

• Monomial function

A polynomial with exactly one term.

• Number line graph of a linear inequality

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

• Replication

The principle of experimental design that minimizes the effects of chance variation by repeating the experiment multiple times.

• Sample space

Set of all possible outcomes of an experiment.

• Transitive property

If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.

• Upper bound for ƒ

Any number B for which ƒ(x) ? B for all x in the domain of ƒ.

• Upper bound test for real zeros

A test for finding an upper bound for the real zeros of a polynomial.