query: Compute $\lim_{n \rightarrow \infty} \sin (n {\pi} {\sqrt[3] {n^{3} + 3n^{2} + 4n - 5}})$
positive_passages.docid: 155303
positive_passages.text: Does $\lim_{n\rightarrow\infty}\sin\left(\pi\sqrt[3]{n^{3}+1}\right)$ exist?
negative_passages.docid: 64860
negative_passages.text: Evaluation of $\lim\limits_{x\rightarrow0} \frac{\tan(x)-x}{x^3}$
negative_passages.docid: 17090
negative_passages.text: Compute $\lim_\limits{n\to\infty}a_n$ where $a_{n+2}=\sqrt{a_n.a_{n+1}}$
negative_passages.docid: 122073
negative_passages.text: Computing $\lim_{n \rightarrow\infty} \int_{a}^{b}\left ( f(x)\left | \sin(nx) \right | \right )$ with $f$ continuous on $[a,b]$
negative_passages.docid: 67853
negative_passages.text: Prove existence of $\lim_{(x,y) \rightarrow (0,2)} \frac{x (y-2)^3}{3x - 5(y-2)^4}$
negative_passages.docid: 57573
negative_passages.text: Evaluate $ \lim_{n\to \infty} ( \lim_{x\to0} (1+\tan^2(x)+\tan^2(2x)+ \cdots + \tan^2(nx)))^{\frac{1}{n^3x^2}} $
negative_passages.docid: 106742
negative_passages.text: Evaluating $ \lim_{x \rightarrow 0}\left (\frac{\sin(x)}{x}\right)^\frac{1}{x^2}$
negative_passages.docid: 155513
negative_passages.text: I need help to advance in the resolution of that limit: $ \lim_{n \to \infty}{\sqrt[n]{\frac{n!}{n^n}}} $
negative_passages.docid: 95718
negative_passages.text: Computing $ \lim_{n\rightarrow \infty}\left(\frac{1^n+2^n+\cdots \cdots +n^n}{n^n}\right)$
negative_passages.docid: 63023
negative_passages.text: Evaluation of $\lim_{x\rightarrow \infty}\sqrt{x^2+x+1} -\lfloor \sqrt{x^2+x+1 }\rfloor\;,$
negative_passages.docid: 65975
negative_passages.text: Calculating $\lim_{n\to\infty}\sqrt{n}\sin(\sin...(\sin(x)..)$
negative_passages.docid: 42241
negative_passages.text: Evaluation of $\lim_{n\rightarrow \infty}\sum^{n}_{r=1}\frac{r}{n^2+n+r}$
negative_passages.docid: 65015
negative_passages.text: Computing $\lim_{n \to \infty} \sqrt[n]{ \int_{0}^{1} (1+x^n)^n dx}$
negative_passages.docid: 82831
negative_passages.text: Evaluating the limit $\lim_{n\to\infty} \left[ \frac{n}{n^2+1}+ \frac{n}{n^2+2^2} + \ldots + \frac{n}{n^2+n^2} \right]$
negative_passages.docid: 155873
negative_passages.text: Evaluate $\lim\limits_{n\rightarrow \infty}\frac{n+n^2+n^3+\cdots +n^n}{1^n+2^n+3^n+\cdots +n^n}.$
negative_passages.docid: 107237
negative_passages.text: Evaluate $\lim_{n\rightarrow\infty} \int_0^1 f(x^n) dx$
negative_passages.docid: 42519
negative_passages.text: $\lim_{n \rightarrow \infty} \sum^n_{k=1} \frac{1}{k+n}$