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(a) ( Use the definitions above to show that tanha da cosha (b) water with depth d is given by The velocity of a water wave with length L moving across a body of 27d tanh 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 u

(a) ( Use the definitions above to show that tanha da cosha (b) water with depth d is given by The velocity of a water wave with length L moving across a body of 27d tanh 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 u

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. 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 e + e cosh z = the "hyperbolic sine function" is given by sinh a and the "hyperbolic tangent function is given by sinh r tanh = Cosh z (a) | Use the definitions above to show that tanh a da cosh (b) water with depth id is given by The velodity of a water wave with length Lmoving across a body of 2nd 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 guestion above. L→∞
Transcribed Image Text: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 e + e cosh z = the "hyperbolic sine function" is given by sinh a and the "hyperbolic tangent function is given by sinh r tanh = Cosh z (a) | Use the definitions above to show that tanh a da cosh (b) water with depth id is given by The velodity of a water wave with length Lmoving across a body of 2nd 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 guestion above. L→∞
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