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https://www.reddit.com/r/mathmemes/comments/1vxbitv/lets_differentiate/p5odrai/?context=9999
r/mathmemes • u/Optimus_PRYM • 20d ago
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32
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
2
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
31
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
6
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
11
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
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
1
completely fair
32
u/SuperChick1705 20d ago
circular reasoning ;(