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Solutions for Chapter 5.5: The Substitution Rule

Full solutions for Single Variable Calculus: Early Transcendentals | 8th Edition

ISBN: 9781305270336

Solutions for Chapter 5.5: The Substitution Rule

Solutions for Chapter 5.5
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ISBN: 9781305270336

This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals, edition: 8. Single Variable Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781305270336. Chapter 5.5: The Substitution Rule includes 94 full step-by-step solutions. Since 94 problems in chapter 5.5: The Substitution Rule have been answered, more than 36094 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Arrow

The notation PQ denoting the directed line segment with initial point P and terminal point Q.

• Combinatorics

A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined

• Convergence of a series

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

• 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

• End behavior asymptote of a rational function

A polynomial that the function approaches as.

• Factored form

The left side of u(v + w) = uv + uw.

• Finite series

Sum of a finite number of terms.

• Index of summation

See Summation notation.

• Inferential statistics

Using the science of statistics to make inferences about the parameters in a population from a sample.

• Inverse of a matrix

The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

• Inverse relation (of the relation R)

A relation that consists of all ordered pairs b, a for which a, b belongs to R.

• Multiplicative inverse of a real number

The reciprocal of b, or 1/b, b Z 0

• Negative linear correlation

See Linear correlation.

• Newton’s law of cooling

T1t2 = Tm + 1T0 - Tm2e-kt

• Permutations of n objects taken r at a time

There are nPr = n!1n - r2! such permutations

• Positive linear correlation

See Linear correlation.

• Solve a triangle

To find one or more unknown sides or angles of a triangle

• Synthetic division

A procedure used to divide a polynomial by a linear factor, x - a

• Vector

An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.

• Work

The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.

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