query: Proof that $\lim_{x \to 0} \frac{\sin(x) - x}{x^2} = 0$ (Without L'Hospital)
positive_passages.docid: 155979
positive_passages.text: $\lim_{x\to 0} \frac{\sin x - x}{x^2}$ without L'Hospital or Taylor
negative_passages.docid: 65239
negative_passages.text: Find $\lim_{x \to 0} \frac{x - \tan(x)}{x - \sin(x)}$
negative_passages.docid: 73786
negative_passages.text: Limit of $\frac{\sin(x+y)}{x+y}$ as $(x,y) \to (0,0)$
negative_passages.docid: 60878
negative_passages.text: How to prove that $\lim_{(x,y) \to (0,0)} \frac{x^3y}{x^4+y^2} = 0?$
negative_passages.docid: 64628
negative_passages.text: Solving limits of a sine wave $\lim_{x\to+\infty}\frac{\sin(x)}{x}$
negative_passages.docid: 78877
negative_passages.text: Limit: $\lim\limits_{x\to0}\frac{e^x-e^{\sin x}}{x-\sin x}$
negative_passages.docid: 13104
negative_passages.text: What is $\lim_{x \to \infty} \frac{\sin x}{\sin x}?$
negative_passages.docid: 59890
negative_passages.text: Fundamental Theorem of Calculus for $\lim\limits_{x\to 0}\frac{\int_0^x(x-t)\sin t^2\ dt}{x\sin^3x}$
negative_passages.docid: 65213
negative_passages.text: How to find $\lim\limits_{x\to0}\frac{e^x-1-x}{x^2}$ without using l'Hopital's rule nor any series expansion?
negative_passages.docid: 156736
negative_passages.text: Prove that $\lim _{x \to \infty} x\sin x$ doesn't exist (using delta epsilon).
negative_passages.docid: 113781
negative_passages.text: How can I calculate $\lim_{x\to 0} \frac{\arctan(x)-\arcsin(x)}{x^3}$ without L'Hôpital?
negative_passages.docid: 124208
negative_passages.text: Proof $|\sin(x) - x| \le \frac{1}{3.2}|x|^3$
negative_passages.docid: 27423
negative_passages.text: Why does $\lim_{x\to 0^+} x^{\sin x}=1$?
negative_passages.docid: 123490
negative_passages.text: L'Hopital's rule and $\frac{\sin x}x$
negative_passages.docid: 136714
negative_passages.text: Proving that $\lim_{x \to 0} \frac{f(x)}{|x|}=1$ implies $f$ is not differentiable at $0$.
negative_passages.docid: 152640
negative_passages.text: show that $\lim(\pi(x)/x) = 0$
negative_passages.docid: 85269
negative_passages.text: Proof that limit of (lnx)/x = 0 without LHopital