 5.9.1: ?In Exercises 16, evaluate the function. If the value is not a rat...
 5.9.2: ?In Exercises 16, evaluate the function. If the value is not a rat...
 5.9.3: ?In Exercises 16, evaluate the function. If the value is not a rat...
 5.9.4: ?In Exercises 16, evaluate the function. If the value is not a rat...
 5.9.5: ?In Exercises 16, evaluate the function. If the value is not a rat...
 5.9.6: ?In Exercises 16, evaluate the function. If the value is not a rat...
 5.9.7: ?In Exercises 714, verify the identity.\(\tanh ^{2} x+\operatornam...
 5.9.8: ?In Exercises 714, verify the identity.\(\operatorname{coth}^{2} x...
 5.9.9: ?In Exercises 714, verify the identity.\(\cosh ^{2} x=\frac{1+\cos...
 5.9.10: ?In Exercises 714, verify the identity.\(\sinh ^{2} x=\frac{1+\co...
 5.9.11: ?In Exercises 714, verify the identity.sinh 2x = 2 sinh x cosh x
 5.9.12: ?In Exercises 714, verify the identity.\(e^{2 x}=\sinh 2 x+\cosh 2...
 5.9.13: ?In Exercises 714, verify the identity.sinh(x + y) = sinh x cosh y...
 5.9.14: ?In Exercises 714, verify the identity.\(\cosh x+\cosh y=2 \cosh \...
 5.9.15: ?In Exercises 15 and 16, use the value of the given hyperbolic func...
 5.9.16: ?In Exercises 15 and 16, use the value of the given hyperbolic func...
 5.9.17: ?In Exercises 1722, find the limit.\(\lim _{x \rightarrow \infty} ...
 5.9.18: ?In Exercises 1722, find the limit.\(\lim _{x \rightarrow\infty} ...
 5.9.19: ?In Exercises 1722, find the limit.\(\lim _{x \rightarrow \infty} ...
 5.9.20: ?In Exercises 1722, find the limit.\(\lim _{x \rightarrow\infty} ...
 5.9.21: ?In Exercises 1722, find the limit.\(\lim _{x \rightarrow 0} \frac...
 5.9.22: ?In Exercises 1722, find the limit.\(\lim _{x \rightarrow 0^{}} \...
 5.9.23: ?In Exercises 2332, find the derivative of the function.f(x) = sin...
 5.9.24: ?In Exercises 2332, find the derivative of the function.f(x) = cos...
 5.9.25: ?In Exercises 2332, find the derivative of the function.\(y=\opera...
 5.9.26: ?In Exercises 2332, find the derivative of the function.\(f(x)=\ta...
 5.9.27: ?In Exercises 2332, find the derivative of the function.f(x) = ln(...
 5.9.28: ?In Exercises 2332, find the derivative of the function.\(y=\ln \l...
 5.9.29: ?In Exercises 2332, find the derivative of the function.\(h(x)=\fr...
 5.9.30: ?In Exercises 2332, find the derivative of the function.y = x cosh...
 5.9.31: ?In Exercises 2332, find the derivative of the function.f(t) = arc...
 5.9.32: ?In Exercises 2332, find the derivative of the function.\(g(x)=\op...
 5.9.33: ?In Exercises 3336, find an equation of the tangent line to graph ...
 5.9.34: ?In Exercises 3336, find an equation of the tangent line to graph ...
 5.9.35: ?In Exercises 3336, find an equation of the tangent line to graph ...
 5.9.36: ?In Exercises 3336, find an equation of the tangent line to graph ...
 5.9.37: ?In Exercises 3740, find any relative extrema of the function. Use...
 5.9.38: ?In Exercises 3740, find any relative extrema of the function. Use...
 5.9.39: ?In Exercises 3740, find any relative extrema of the function. Use...
 5.9.40: ?In Exercises 3740, find any relative extrema of the function. Use...
 5.9.41: ?In Exercises 41 and 42, a model for a power cable suspended betwee...
 5.9.42: ?In Exercises 41 and 42, a model for a power cable suspended betwee...
 5.9.43: ?In Exercises 4354, find the indefinite integral.\(\int \cosh 2 x ...
 5.9.44: ?In Exercises 4354, find the indefinite integral.\(\int \operatorn...
 5.9.45: ?In Exercises 4354, find the indefinite integral.\(\int \sinh (12...
 5.9.46: ?In Exercises 4354, find the indefinite integral.\(\int \frac{\cos...
 5.9.47: ?In Exercises 4354, find the indefinite integral.\(\int \cosh ^{2}...
 5.9.48: ?In Exercises 4354, find the indefinite integral.\(\int \frac{\sin...
 5.9.49: ?In Exercises 4354, find the indefinite integral.\(\int \frac{\cos...
 5.9.50: ?In Exercises 4354, find the indefinite integral.\(\int \operatorn...
 5.9.51: ?In Exercises 4354, find the indefinite integral.\(\int x \operato...
 5.9.52: ?In Exercises 4354, find the indefinite integral.\(\int \operatorn...
 5.9.53: ?In Exercises 4354, find the indefinite integral.\(\int \frac{\ope...
 5.9.54: ?In Exercises 4354, find the indefinite integral.\(\int \frac{\cos...
 5.9.55: ?In Exercises 5560, evaluate the integral.\(\int_{0}^{\ln 2} \tanh...
 5.9.56: ?In Exercises 5560, evaluate the integral.\(\int_{0}^{1} \cosh ^{2...
 5.9.57: ?In Exercises 5560, evaluate the integral.\(\int_{0}^{4} \frac{1}{...
 5.9.58: ?In Exercises 5560, evaluate the integral.\(\int_{0}^{4} \frac{1}{...
 5.9.59: ?In Exercises 5560, evaluate the integral.\(\int_{0}^{\sqrt{2} / 4...
 5.9.60: ?In Exercises 5560, evaluate the integral.\(\int_{0}^{\ln 2} 2 e^{...
 5.9.61: Comparing Functions Discuss several ways in which the hyperbolic fu...
 5.9.62: Hyperbolic Functions Which hyperbolic functions take on only positi...
 5.9.63: Comparing Derivative Formulas Which hyperbolic derivative formulas ...
 5.9.64: ?Use the graphs of f and g shown in the figures to answer the follo...
 5.9.65: ?In Exercises 6574, find the derivative of the function.\(y=\cosh ...
 5.9.66: ?In Exercises 6574, find the derivative of the function.\(y=\tanh ...
 5.9.67: ?In Exercises 6574, find the derivative of the function.\(y=\tanh ...
 5.9.68: ?In Exercises 6574, find the derivative of the function.\(f(x)=\op...
 5.9.69: ?In Exercises 6574, find the derivative of the function.\(y=\sinh ...
 5.9.70: ?In Exercises 6574, find the derivative of the function.\(y=\tanh ...
 5.9.71: ?In Exercises 6574, find the derivative of the function.\(y=\left(...
 5.9.72: ?In Exercises 6574, find the derivative of the function.\(y=\opera...
 5.9.73: ?In Exercises 6574, find the derivative of the function.\(y=2 x \s...
 5.9.74: ?In Exercises 6574, find the derivative of the function.\(y=x \tan...
 5.9.75: ?In Exercises 7582, find the indefinite integral using the formula...
 5.9.76: ?In Exercises 7582, find the indefinite integral using the formula...
 5.9.77: ?In Exercises 7582, find the indefinite integral using the formula...
 5.9.78: ?In Exercises 7582, find the indefinite integral using the formula...
 5.9.79: ?In Exercises 7582, find the indefinite integral using the formula...
 5.9.80: ?In Exercises 7582, find the indefinite integral using the formula...
 5.9.81: ?In Exercises 7582, find the indefinite integral using the formula...
 5.9.82: ?In Exercises 7582, find the indefinite integral using the formula...
 5.9.83: ?In Exercises 8386, evaluate the definite integral using the formu...
 5.9.84: ?In Exercises 8386, evaluate the definite integral using the formu...
 5.9.85: ?In Exercises 8386, evaluate the definite integral using the formu...
 5.9.86: ?In Exercises 8386, evaluate the definite integral using the formu...
 5.9.87: ?In Exercises 8790, solve the differential equation.\(\frac{d y}{d...
 5.9.88: ?In Exercises 8790, solve the differential equation.\(\frac{d y}{d...
 5.9.89: ?In Exercises 8790, solve the differential equation.\(\frac{d y}{d...
 5.9.90: ?In Exercises 8790, solve the differential equation.\(\frac{d y}{d...
 5.9.91: ?In Exercises 91–94, find the area of the region.\(y=\operatorname{...
 5.9.92: ?In Exercises 91–94, find the area of the region.y = tanh 2x
 5.9.93: ?In Exercises 91–94, find the area of the region.\(y=\frac{5 x}{\sq...
 5.9.94: ?In Exercises 91–94, find the area of the region.\(y=\frac{6}{\sqrt...
 5.9.95: ?Chemicals A and B combine in a 3 to 1 ratio to form a compound. ...
 5.9.96: ?An object is dropped from a height of 400 feet.(a) Find the veloci...
 5.9.97: ?Consider the equation of the tractrix \(y=a \operatorname{sech}^{...
 5.9.98: Tractrix Show that the boat in Example 5 is always pointing toward ...
 5.9.99: ?Prove that\(\tanh ^{1} x=\frac{1}{2} \ln \left(\frac{1+x}{1x}\ri...
 5.9.100: ?Prove that\(\sinh ^{1} t=\ln \left(t+\sqrt{t^{2}+1}\right)\).Text...
 5.9.101: ?Show thatarctan (sinh x) = arcsin (tanh x) .
 5.9.102: ?Let x > 0 and b > 0. Show that\(\int_{b}^{b} e^{x t} d t=\frac{2 ...
 5.9.103: ?In Exercises 103105, prove the differentiation formula.\(\frac{d}...
 5.9.104: ?In Exercises 103105, prove the differentiation formula.\(\frac{d}...
 5.9.105: ?In Exercises 103105, prove the differentiation formula.\(\frac{d}...
 5.9.106: ?In Exercises 106108, verify the differentiation formula.\(\frac{d...
 5.9.107: ?In Exercises 106108, verify the differentiation formula.\(\frac{d...
 5.9.108: ?In Exercises 106108, verify the differentiation formula.\(\frac{d...
 5.9.109: ?From the vertex (0, c) of the catenary y = c cosh(x/c) a line L is...
 5.9.110: ?Prove or disprove: there is at least one straight line normal to t...
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
Get Full SolutionsChapter 5.9: Hyperbolic Functions includes 110 full stepbystep solutions. Since 110 problems in chapter 5.9: Hyperbolic Functions have been answered, more than 182683 students have viewed full stepbystep 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.

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 yaxis 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.

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

Zero factorial
See n factorial.