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(e) Solve for x 4 + sinh(3x) = 4 cosh(3x). (f) Using Euler's formula, ei = cos 0 +j sin 0, derive the following relationships between the hyperbolic and trigonometric functions (i) sin(jx) = j sinh(x). (ii) cos(jx) = cosh(x). %3D

(e) Solve for x 4 + sinh(3x) = 4 cosh(3x). (f) Using Euler's formula, ei = cos 0 +j sin 0, derive the following relationships between the hyperbolic and trigonometric functions (i) sin(jx) = j sinh(x). (ii) cos(jx) = cosh(x). %3D

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 57SE: Repeat the previous exercise to find the formula forthe APY of an account that compounds daily....
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Question 2 (a) Define the following hyperbolic functions directly in terms of the exponential function (i) sinh(x). (ii) cosh(x). (iii) tanh(x). (b) Sketch, on separate graphs, each of the functions in part (a). (c) Prove, using the definitions of sinh and cosh in terms of the exponential function, that cosh(2x) = cosh?(x) + sinh²(x). (d) Derive the formula 1+ X In 2 1 tanh-'(x) 1 - x (e) Solve for x 4 + sinh(3x) = 4 cosh(3x). (f) Using Euler's formula, el = cos 0 + j sin 0, derive the following relationships between the hyperbolic and trigonometric functions (i) sin(jx) = j sinh(x). (ii) cos(jx) = cosh(x).
Transcribed Image Text:Question 2 (a) Define the following hyperbolic functions directly in terms of the exponential function (i) sinh(x). (ii) cosh(x). (iii) tanh(x). (b) Sketch, on separate graphs, each of the functions in part (a). (c) Prove, using the definitions of sinh and cosh in terms of the exponential function, that cosh(2x) = cosh?(x) + sinh²(x). (d) Derive the formula 1+ X In 2 1 tanh-'(x) 1 - x (e) Solve for x 4 + sinh(3x) = 4 cosh(3x). (f) Using Euler's formula, el = cos 0 + j sin 0, derive the following relationships between the hyperbolic and trigonometric functions (i) sin(jx) = j sinh(x). (ii) cos(jx) = cosh(x).
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