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# Solutions for Chapter 5.9: Hyperbolic Functions

## Full solutions for Calculus: Early Transcendental Functions | 6th Edition

ISBN: 9781285774770

Solutions for Chapter 5.9: Hyperbolic Functions

Solutions for Chapter 5.9
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##### ISBN: 9781285774770

Chapter 5.9: Hyperbolic Functions includes 110 full step-by-step solutions. Since 110 problems in chapter 5.9: Hyperbolic Functions have been answered, more than 182683 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9781285774770. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions, edition: 6.

Key Calculus Terms and definitions covered in this textbook
• Additive identity for the complex numbers

0 + 0i is the complex number zero

• Center

The central point in a circle, ellipse, hyperbola, or sphere

• Combinations of n objects taken r at a time

There are nCr = n! r!1n - r2! such combinations,

• Commutative properties

a + b = b + a ab = ba

• Difference of two vectors

<u1, u2> - <v1, v2> = <u1 - v1, u2 - v2> or <u1, u2, u3> - <v1, v2, v3> = <u1 - v1, u2 - v2, u3 - v3>

• Domain of validity of an identity

The set of values of the variable for which both sides of the identity are defined

• Even function

A function whose graph is symmetric about the y-axis for all x in the domain of ƒ.

• Limit

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

• Mathematical model

A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

• Positive linear correlation

See Linear correlation.

• Pythagorean

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

• Reflection through the origin

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

• Regression model

An equation found by regression and which can be used to predict unknown values.

• Residual

The difference y1 - (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.

• Sinusoid

A function that can be written in the form f(x) = a sin (b (x - h)) + k or f(x) = a cos (b(x - h)) + k. The number a is the amplitude, and the number h is the phase shift.

• Sinusoidal regression

A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

• Solve algebraically

Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator

• Vertical translation

A shift of a graph up or down.

• x-axis

Usually the horizontal coordinate line in a Cartesian coordinate system with positive direction to the right,.

• Zero factorial

See n factorial.