Hyperbolic Functions 2
? Maplesoft, a division of Waterloo Maple Inc., 2007
Introduction
This application is one of a collection of examples teaching Calculus with Maple. These applications use Clickable Calculus? methods to solve problems interactively. Steps are given at every stage of the solution, and many are illustrated using short video clips. Click on the
buttons to watch the videos.
The steps in the document can be repeated to solve similar problems.
Problem Statement
Obtain the logarithmic form of 
, the functional inverse of 
.
Solution
Step
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Result
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Enter  and convert it to exponential form.
Enter  and press [Enter]. Right-click, Conversions>Exponential.
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 |
(3.1) |
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(3.2) |
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Let  represent the exponential form of  .
Use the equation label for the exponential expression of  ([Ctrl]+L, type the equation number and press [Enter].
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 |
(3.3) |
|
Solve for 
Copy the equation above (use [Ctrl]-drag) to a new document block. Let  and edit the equation appropriately. Press [Enter]. Right-click, Solve>Obtain solutions for>u.
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 |
(3.4) |
 
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Consider the positive solution for  .
Set  and solve for 
Use the template  template in the Expression palette and the equation number for the positive solution of  to form the equation. (Typing "e" does not generate the base of the exponential function. Use the Palette.)
Right-click, Solve>Obtain Solutions for> .
Right-click, Evaluate at a point, set  , [Enter].
Alternatively, copy the solution for  ([Ctrl]-drag) to a new line and change  to  and  to  .
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(3.5) |
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(3.6) |
 
 
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