query: How do i solve this limit: $\lim_{x\to 0}{x-\sin(\sin(...(\sin x)))\over x^{3}}$
positive_passages.docid: 24076
positive_passages.text: Evaluating limit (iterated sine function)
negative_passages.docid: 150981
negative_passages.text: Why doesn't using the approximation $\sin x\approx x$ near $0$ work for computing this limit?
negative_passages.docid: 45728
negative_passages.text: Proving a limit of a trigonometric function: $\lim_{x \to 2/\pi}\lfloor \sin \frac{1}{x} \rfloor=0$
negative_passages.docid: 156610
negative_passages.text: To prove the limit of $\frac{x^2+2\cos x-2}{x\sin^3 x}$ at zero is $1/12$
negative_passages.docid: 86169
negative_passages.text: How do I solve this limit: $\lim _{x \to 0} \left(\frac{ \sin x}{x}\right)^{1/x}$?
negative_passages.docid: 125087
negative_passages.text: Evaluate the limit of ratio of sums of sines (without L'Hopital): $\lim_{x\to0} \frac{\sin x+\sin3x+\sin5x}{\sin2x+\sin4x+\sin6x}$
negative_passages.docid: 103218
negative_passages.text: Find $\lim_{(x,y) \to (0,0)} \frac{\tan(x^3+y^3)}{\sin(x^2+y^2)}$
negative_passages.docid: 73295
negative_passages.text: Limit approaching infinity of sine function
negative_passages.docid: 80314
negative_passages.text: Finding $\lim\limits_{x\to 0}\frac{\sin{3x}}{x}$
negative_passages.docid: 32572
negative_passages.text: What is $\lim_{(x,y)\to(0,0)} \frac{(x^3+y^3)}{(x^2-y^2)}$?
negative_passages.docid: 81537
negative_passages.text: Limit: $\lim_{x\to 0}\frac{\tan3x}{\sin2x}$
negative_passages.docid: 155303
negative_passages.text: Does $\lim_{n\rightarrow\infty}\sin\left(\pi\sqrt[3]{n^{3}+1}\right)$ exist?
negative_passages.docid: 112481
negative_passages.text: Given $a_{n+1} = \frac{{a_n}}{\sin({a_n})}$ with $0 < a_1 < \frac{\pi}{2}$. Show that the limit $\lim_{n\rightarrow\infty}{a_n}$ exists and find it.
negative_passages.docid: 123568
negative_passages.text: Solving limit given a limit
negative_passages.docid: 100893
negative_passages.text: Determine $\lim_{x \to 0}{\frac{x-\sin{x}}{x^3}}=\frac{1}{6}$, without L'Hospital or Taylor
negative_passages.docid: 27423
negative_passages.text: Why does $\lim_{x\to 0^+} x^{\sin x}=1$?
negative_passages.docid: 7819
negative_passages.text: Calculate: $ \lim_{x \to 0 } = x \cdot \sin(\frac{1}{x}) $