Hyperbolic Functions: Graphing cosh(x) - (Revisited)

In this video I revisit my earlier graphing cosh(x) video to provide some further intriguing and unique observations of hyperbolic functions at larger scales. But just in the previous video, I go over the hyperbolic cosine or cosh(x) function and sketch the curve of it manually, as well as determining the domain and range, minimum and maximum points, and concavity. I use the methods obtain from my earlier video on Guidelines for Sketching to go about determining just how the shape of the cosh(x) looks like. In the previous video I compared cosh(x) with a basic parabolic function to show that although they look similar, but this was only for low values of y! At low values the cosh(x) initially is more broad in terms of steepness but then gradually becomes more steep than x^2. But when the scale is changed, the difference becomes quite clear. The cosh(x) functions increases at a much faster rate relative to both x^2 and the x-values themselves. Thus even when cosh(x) is equal to large values such as 200,000 the values of x are still around only 10. Thus when graphing both cosh(x) and x^2 together at these large values, the parabolic function appears as a horizontal line! This is quite an amazing feature of hyperbolic cosine, and thus I had to revisit this video to illustrate the fact that we need to always compare functions at multiple different scales; so make sure to watch this eye-opening video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhv4_KAVjBkaGN4fOvQ

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-hyperbolic-functions-graphing-cosh-x-revisited

Related Videos:

Hyperbolic Functions - tanh(x), sinh(x), cosh(x) - Introduction: http://youtu.be/EmJKuQBEdlc
Guidelines to Curve Sketching: http://youtu.be/tOn7ZSAntKs
Conic Sections: Parabolas: Definition and Formula: https://youtu.be/kCJjXuuIqbE .

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