Question

Simplify the expressions. $$\cosh (\ln t)$$

Name: Problem 15, Chapter 3: Calculus Single Variable
Uploaded: 2021-04-27T07:36:09-08:00
Duration: 1 min 17 s
Channel: Tyler Moulton
Description: Simplify the expressions. cosh(lnt)

   Simplify the expressions.
$$\cosh (\ln t)$$

Calculus Single Variable

Deborah… 7th Edition

Chapter 3, Problem 15

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Solved by Expert Tyler Moulton

04/27/2021

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Simplify the expressions. $$\cosh (\ln t)$$

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Key Concepts

Hyperbolic Cosine Function

The hyperbolic cosine function is defined as cosh(x) = (e^x + e^(–x))/2. This function appears in many areas of mathematics, including calculus, differential equations, and hyperbolic geometry, and it serves as a counterpart to the trigonometric cosine but with the exponential function.

Exponential and Logarithmic Relationship

Exponential and logarithmic functions are inverse functions. This key relationship, expressed as e^(ln t) = t, allows one to simplify expressions where logarithms are in the argument of exponential or hyperbolic functions, enabling the transformation of complex expressions into simpler algebraic forms.

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