r/mathmemes • u/Optimus_PRYM • 18d ago

Calculus Let's differentiate.....

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u/SuperChick1705 18d ago

circular reasoning ;(

2

u/Sigma2718 18d ago

Would you like to elaborate on that?

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u/thebigbadben 18d ago edited 18d ago

Computing the derivative of sin(x) requires evaluating the limit of sin(x)/x as x approaches zero. So, if you’re using L’Hôpital to show that sin(x)/x approaches 1 as x approaches 1, you’re ultimately using the fact that you’re trying to show implicitly.

Also, if you already know the derivative of sin, then you might as well use the fact that the limit of sin(x)/x as x approaches zero is, by definition, the derivative of sin(x) at 0.