Weirdness is in graphs!

As you all already know how the graph of f(x)=sin⁡xxf\left(x\right)=\frac{\sin x}{x} looks like, try graphing f(x)=sin⁡(1(x))1xf\left(x\right)=\frac{\sin \left(\frac{1}{\left(x\right)}\right)}{\frac{1}{x}}. (Yes! You're allowed to graph it using an electronic graphing calculator, or use the Desmos Graphing Calculator.)

Try graphing the following too!

tan⁡(xcos⁡(1x))\tan \left(\frac{x}{\cos \left(\frac{1}{x}\right)}\right)

tan⁡(x(sec⁡x))\tan \left(\frac{x}{\left(\sec x\right)}\right). (Nothing? Zoom out for the climax!)

The bombshell:

sin⁡(cos⁡(tan⁡(csc⁡(sec⁡(cot⁡(arcsin⁡(arccos⁡(arctan⁡(arccsc⁡(arcsec⁡(arccot⁡(x)))))))))))) \sin \left(\cos \left(\tan \left(\csc \left(\sec \left(\cot \left(\arcsin \left(\arccos \left(\arctan \left(\operatorname{arccsc}\left(\operatorname{arcsec}\left(\operatorname{arccot}\left(x\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)

And your device starts lagging a bit too as you move towards the negative x-axis.

exln⁡(sin⁡(ecos⁡(1(((x))))))\frac{e^x}{\ln \left(\sin \left(e^{\cos \left(\frac{1}{\left(\left(\left(x\right)\right)\right)}\right)}\right)\right)}

Seems as if the curve is a fan of the negative y-axis!

sin⁡(1e1arccsc⁡(x))\sin \left(\frac{1}{e^{\frac{1}{\operatorname{arccsc}\left(x\right)}}}\right)

Kindly move towards the negative x-axis.

yx=sec⁡(20x) y^x=\sec \left(20x\right)

Clearly, this time the graphing calculator gave up!

You're free to share any such function which has such a peculiar curve in the comments section. Cheers! :D

GIF Credit: Reddit

#Calculus

Note by Arkajyoti Banerjee
4 years, 10 months ago

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Comments

Weird weird weird!!!

Athenkosi Bezana - 4 years, 10 months ago
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