query: Simple calculus question: is applying l'Hopital's rule to $\sin(x) / x$ really circular reasoning?
positive_passages.docid: 154080
positive_passages.text: circular reasoning in proving $\frac{\sin x}x\to1,x\to0$
negative_passages.docid: 113086
negative_passages.text: Prove or disprove that $f(x) = \sin x/x$ is uniformly continuous over the interval $(0,1)$?
negative_passages.docid: 40556
negative_passages.text: Why is $\sin(\alpha+\beta)=\sin\alpha\cos\beta+\sin\beta\cos\alpha$
negative_passages.docid: 108918
negative_passages.text: Can someone explain this trigonometric limit?
negative_passages.docid: 46642
negative_passages.text: Continuity of $\sin(x)/x$
negative_passages.docid: 156448
negative_passages.text: Evaluate the limit without using the L'Hôpital's rule
negative_passages.docid: 61242
negative_passages.text: L'Hôpital's rule does not apply?!
negative_passages.docid: 3948
negative_passages.text: Why do we require radians in calculus?
negative_passages.docid: 125812
negative_passages.text: Is sin(x) necessarily irrational where x is rational?
negative_passages.docid: 40235
negative_passages.text: How would I differentiate $\sin{x}^{\cos{x}}?$
negative_passages.docid: 70086
negative_passages.text: Limit without l'Hopital or Taylor series: $\lim\limits_{x \to 0} \frac{x\cos x- \sin x}{x^3}$
negative_passages.docid: 102730
negative_passages.text: Is my proof correct? (Conformal equivalence of two circular annuli)
negative_passages.docid: 128795
negative_passages.text: $n$th derivative of $e^x \sin x$
negative_passages.docid: 97213
negative_passages.text: Why does $\sin(0)$ exist?
negative_passages.docid: 53307
negative_passages.text: how to strictly prove $\sin x<x$ for $0<x<\frac{\pi}{2}$
negative_passages.docid: 49444
negative_passages.text: Why isn't $e^{2\pi xi}=1$ true for all $x$?
negative_passages.docid: 116013
negative_passages.text: Problem applying L'Hopitals rule.