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6. The "hyperbolic trigonometric functions" are specific combinations of ex- ponential functions that appear in application frequently enough that they have their own names. For example, the "hyperbolic cosine function" is given by et +e-x cosh x 2 the "hyperbolic sine function" is given by et - e-a sinh x = and the "hyperbolic tangent function" is given by sinh x tanh x = cosh x Use the definitions above to show that d tanh x = dx 1 cosh x

6. The "hyperbolic trigonometric functions" are specific combinations of ex- ponential functions that appear in application frequently enough that they have their own names. For example, the "hyperbolic cosine function" is given by et +e-x cosh x 2 the "hyperbolic sine function" is given by et - e-a sinh x = and the "hyperbolic tangent function" is given by sinh x tanh x = cosh x Use the definitions above to show that d tanh x = dx 1 cosh x

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 80E
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6. S). The "hyperbolic trigonometric functions" are specific combinations of ex- ponential functions that appear in application frequently enough that they have their own names. For example, the "hyperbolic cosine function" is given by et + e- cosh x = the "hyperbolic sine function" is given by et e - sinh x = and the "hyperbolic tangent function" is given by sinh x tanh x = cosh x (a) Use the definitions above to show that d tanh x = dx 1 cosh x
Transcribed Image Text:6. S). The "hyperbolic trigonometric functions" are specific combinations of ex- ponential functions that appear in application frequently enough that they have their own names. For example, the "hyperbolic cosine function" is given by et + e- cosh x = the "hyperbolic sine function" is given by et e - sinh x = and the "hyperbolic tangent function" is given by sinh x tanh x = cosh x (a) Use the definitions above to show that d tanh x = dx 1 cosh x
(b) water with depth d is given by The velocity of a water wave with length L moving across a body of gL tanh 27 2πd V = where g represents the acceleration due to gravity (a positive constant). What happens to the velocity as the wave length increases without bound? That is, evaluate lim v Hint: Find lim v2 first, and then use that to answer the question above.
Transcribed Image Text:(b) water with depth d is given by The velocity of a water wave with length L moving across a body of gL tanh 27 2πd V = where g represents the acceleration due to gravity (a positive constant). What happens to the velocity as the wave length increases without bound? That is, evaluate lim v Hint: Find lim v2 first, and then use that to answer the question above.
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