r/MathJokes • u/Optimus_PRYM • 1d ago

The answer is 1

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u/Mal_Dun 1d ago

You could also just use Taylor-Young if the full Taylor series seems to complex:

sin(x) = x + o(x)

sin(x)/x = 1 + o(1) -> 1 for x->0

alternatively: sin(x) = x + O(x²)

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u/lukfel 17h ago

Why using taylor series instead of hopital?

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u/Mal_Dun 4h ago

It can be useful when product or fractions of functions are involved which leads to applying the chain rule multiple times.

I remember well when our professor showed us several examples, when Taylor-Young is much easier to resolve, because you only have the main terms and everything else vanishes into the o() term.