 3.11.1: Find the numerical value of each expression. (a) sinh 0 (b) cosh 0
 3.11.2: Find the numerical value of each expression. (a) tanh 0 (b) tanh 1
 3.11.3: Find the numerical value of each expression. (a) coshsln 5d (b) cosh 5
 3.11.4: Find the numerical value of each expression. (a) sinh 4 (b) sinhsln 4d
 3.11.5: Find the numerical value of each expression. (a) sech 0 (b) cosh21 1
 3.11.6: Find the numerical value of each expression. . (a) sinh 1 (b) sinh21 1
 3.11.7: Prove the identity. sinhs2xd 2sinh x (This shows that sinh is an od...
 3.11.8: Prove the identity. coshs2xd cosh x (This shows that cosh is an eve...
 3.11.9: Prove the identity. cosh x 1 sinh x ex
 3.11.10: Prove the identity.cosh x 2 sinh x e2x
 3.11.11: Prove the identity. sinhsx 1 yd sinh x cosh y 1 cosh x sinh y
 3.11.12: Prove the identity.coshsx 1 yd cosh x cosh y 1 sinh x sinh y
 3.11.13: Prove the identity. coth2 x 2 1 csch2 x
 3.11.14: Prove the identity. tanhsx 1 yd tanh x 1 tanh y 1 1 tanh x tanh y
 3.11.15: Prove the identity.sinh 2x 2 sinh x cosh x
 3.11.16: Prove the identity.cosh 2x cosh2 x 1 sinh2 x
 3.11.17: Prove the identity.tanhsln xd x 2 2 1 x 2 1 1
 3.11.18: Prove the identity.1 tanh x 1 2 tanh x e 2x
 3.11.19: Prove the identity. scosh x 1 sinh xd n cosh nx 1 sinh nx (n any re...
 3.11.20: If tanh x 12 13, find the values of the other hyperbolic functions ...
 3.11.21: If cosh x 5 3 and x . 0, find the values of the other hyperbolic fu...
 3.11.22: (a) Use the graphs of sinh, cosh, and tanh in Figures 13 to draw th...
 3.11.23: Use the definitions of the hyperbolic functions to find each of the...
 3.11.24: Prove the formulas given in Table 1 for the derivatives of the func...
 3.11.25: Give an alternative solution to Example 3 by letting y sinh21 x and...
 3.11.26: Prove Equation 4.
 3.11.27: Prove Equation 5 using (a) the method of Example 3 and (b) Exercise...
 3.11.28: For each of the following functions (i) give a definition like thos...
 3.11.29: Prove the formulas given in Table 6 for the derivatives of the foll...
 3.11.30: Find the derivative. Simplify where possible. fsxd ex cosh x
 3.11.31: Find the derivative. Simplify where possible. fsxd tanh sx
 3.11.32: Find the derivative. Simplify where possible. tsxd sinh2 x
 3.11.33: Find the derivative. Simplify where possible. hsxd sinhsx 2 d
 3.11.34: Find the derivative. Simplify where possible. Fstd lnssinh td
 3.11.35: Find the derivative. Simplify where possible.Gstd sinhsln td
 3.11.36: Find the derivative. Simplify where possible. y sech x s1 1 ln sech xd
 3.11.37: Find the derivative. Simplify where possible. y ecosh 3x
 3.11.38: Find the derivative. Simplify where possible. fstd 1 1 sinh t 1 2 s...
 3.11.39: Find the derivative. Simplify where possible.tstd t coth st 2 1 1
 3.11.40: Find the derivative. Simplify where possible. y sinh21 stan xd
 3.11.41: Find the derivative. Simplify where possible. y cosh21 sx
 3.11.42: Find the derivative. Simplify where possible.y x tanh21 x 1 ln s1 2...
 3.11.43: Find the derivative. Simplify where possible.y x sinh21 sxy3d 2 s9 ...
 3.11.44: Find the derivative. Simplify where possible. y sech21 se2x d
 3.11.45: Find the derivative. Simplify where possible. y coth21 ssec xd
 3.11.46: Show that d dx 4 1 1 tanh x 1 2 tanh x 1 2 exy2 .
 3.11.47: Show that d dx arctanstanh xd sech 2x.
 3.11.48: The Gateway Arch in St. Louis was designed by Eero Saarinen and was...
 3.11.49: If a water wave with length L moves with velocity v in a body of wa...
 3.11.50: A flexible cable always hangs in the shape of a catenary y c 1 a co...
 3.11.51: A telephone line hangs between two poles 14 m apart in the shape of...
 3.11.52: Using principles from physics it can be shown that when a cable is ...
 3.11.53: A cable with linear density 2 kgym is strung from the tops of two p...
 3.11.54: A model for the velocity of a falling object after time t is vstd m...
 3.11.55: (a) Show that any function of the form y A sinh mx 1 B cosh mx sati...
 3.11.56: If x lnssec 1 tan d, show that sec cosh x.
 3.11.57: At what point of the curve y cosh x does the tangent have slope 1?
 3.11.58: Investigate the family of functions fnsxd tanhsn sin xd where n is ...
 3.11.59: Show that if a 0 and b 0, then there exist numbers and such that ae...
Solutions for Chapter 3.11: Hyperbolic Functions
Full solutions for Single Variable Calculus: Early Transcendentals  8th Edition
ISBN: 9781305270336
Solutions for Chapter 3.11: Hyperbolic Functions
Get Full SolutionsThis 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. Since 59 problems in chapter 3.11: Hyperbolic Functions have been answered, more than 107086 students have viewed full stepbystep solutions from this chapter. Chapter 3.11: Hyperbolic Functions includes 59 full stepbystep solutions. Single Variable Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781305270336.

Acute angle
An angle whose measure is between 0° and 90°

Additive identity for the complex numbers
0 + 0i is the complex number zero

Coordinate(s) of a point
The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian threedimensional space

Course
See Bearing.

Divergence
A sequence or series diverges if it does not converge

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

Equal matrices
Matrices that have the same order and equal corresponding elements.

Inverse sine function
The function y = sin1 x

Leading coefficient
See Polynomial function in x

Matrix element
Any of the real numbers in a matrix

Measure of center
A measure of the typical, middle, or average value for a data set

Outliers
Data items more than 1.5 times the IQR below the first quartile or above the third quartile.

Real axis
See Complex plane.

Reflection across the xaxis
x, y and (x,y) are reflections of each other across the xaxis.

Remainder polynomial
See Division algorithm for polynomials.

Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt

Terminal side of an angle
See Angle.

Trichotomy property
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.

Viewing window
The rectangular portion of the coordinate plane specified by the dimensions [Xmin, Xmax] by [Ymin, Ymax].

Ymax
The yvalue of the top of the viewing window.