step 1 Okay, so we have here F of T is equal to Kosh B of T. So we are asked to get its Laplace transfo

Question

$$\cosh b t$$

Name: Problem 11, Chapter 7: Fundamentals of Differential Equations
Uploaded: 2020-08-04T01:11:14-08:00
Duration: 1 min 34 s
Channel: Cyrielle Lorio
Description: coshb t

   $$\cosh b t$$

Fundamentals of Differential Equations

R. Kent Nagle 9th Edition

Chapter 7, Problem 11

Instant Answer

Solved by Expert Cyrielle Lorio

08/04/2020

Step 1

The hyperbolic cosine function, $\cosh(bt)$, can be expressed as: $$\cosh(bt) = \frac{e^{bt} + e^{-bt}}{2}$$ Show more…

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$$\cosh b t$$

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Key Concepts

Hyperbolic Functions

Hyperbolic functions are analogues of the trigonometric functions but for a hyperbola rather than a circle. They are defined in terms of the exponential function and include cosh, sinh, and tanh, each playing a critical role in calculus, differential equations, and hyperbolic geometry.

Hyperbolic Cosine

The hyperbolic cosine function, written as cosh(x), is defined as (e^x + e^(-x))/2. It is an even function with a characteristic 'catenary' shape and appears in various contexts such as the solution to certain differential equations and the description of the curve of a hanging cable.

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