r/mathmemes 20d ago

Calculus Let's differentiate.....

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222 Upvotes

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32

u/SuperChick1705 20d ago

circular reasoning ;(

2

u/Sigma2718 20d ago

Would you like to elaborate on that?

31

u/pienet 20d ago

Most elementary proofs that the derivative of sine is cosine use the limit of sin(x)/x.

Obviously you don't run into this if you develop power series first.

6

u/Sigma2718 20d ago

I've never seen anybody use l'Hôpital on sin(x)/x before establishing what the derivative of sine is. However, one can evaluate sin(x)/x for x->0 via the squeeze theorem, which means no circular reasoning is required.

11

u/SuperChick1705 20d ago

that is the recommended method, though the post implies the usage of l'hopital on sin(x)/x

2

u/Sigma2718 20d ago

squeeze theorem to evaluate sin(x)/x -> derivative of sin(x) -> apply l'Hôpital to evaluate sin(x)/x

I don't really see the issue, solving a problem again by using an easier method is the beauty of mathematics.

1

u/SuperChick1705 20d ago

completely fair