In this video I go over further into the Catenary hyperbolic function and this time look at an example that involves a reverse derivation of the formula. The reverse calculation involves being given the solution to the differential equation for a catenary, that is a cable hanging by its own weight and hung at two equal heights, which I derived in my earlier video. To prove this I show how we can simply find the first and second derivatives of the solution, which we can then plug into the differential equation. Doing so I show that the left hand side (LHS) and the right hand side (RHS) are equivalent, and thus we have our proof. This is an interesting video to see how we can double check whether a solution we derive is correct by doing some back-calculations, so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvpNbBbZ3XsToMGlQw
View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-hyperbolic-functions-catenary-example-1-reverse-proof
Hyperbolic Functions - tanh(x), sinh(x), cosh(x) - Introduction: http://youtu.be/EmJKuQBEdlc
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Hyperbolic Functions: Catenary: Formula and Proof: https://youtu.be/EYb1p9r1fnM
Derivatives of Hyperbolic Trigonometry: sinh(x): http://youtu.be/9QpIDqYg52c
Derivatives of Hyperbolic Trigonometry: cosh(x): http://youtu.be/4AGkxTGxASQ
Hyperbolic Trigonometry Identity Proof: cosh2(x) - sinh2(x) = 1: http://youtu.be/-UXUqIWRNEA .
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