query: Limit of function using L'Hôpital's rule: $\lim_{x \to \infty}{x-x^2\ln(1+\frac{1}{x})}$
positive_passages.docid: 113913
positive_passages.text: using L'Hospital solve $\lim_{x \to \infty} x - x^{2}\ln(1 + \frac{1}{x})$
negative_passages.docid: 135565
negative_passages.text: Limit of $\frac{1}{x^2}-\frac{1}{\sin^2(x)}$ as $x$ approaches $0$
negative_passages.docid: 101716
negative_passages.text: Find this limit: $ \lim_{n \to \infty}{(e^{\frac{1}{n}} - \frac{2}{n})^n}$
negative_passages.docid: 56085
negative_passages.text: Calculate the limit : $\lim_{x \to 0}\frac{x-\sin{x}}{x^3}$ WITHOUT using L'Hopital's rule
negative_passages.docid: 9746
negative_passages.text: Determine the following limit as x approaches 0: $\frac{\ln(1+x)}x$
negative_passages.docid: 51231
negative_passages.text: Find the limit of $\frac{n^{x}}{(1 + x)^{n}}$
negative_passages.docid: 46156
negative_passages.text: How to find $\lim_{x \to \infty} [x]/x$?
negative_passages.docid: 113336
negative_passages.text: Limit of $(\frac{1}{n^2})^{(\frac{1}{n})}$
negative_passages.docid: 33372
negative_passages.text: What is $\lim_{x\to\infty}\left(\sin{\frac 1x}+\cos{\frac 1x}\right)^x$?
negative_passages.docid: 65275
negative_passages.text: Finding $\lim\limits_{x\to1^-}\Bigl(\prod\limits_{n=0}^{\infty}\Bigl(\frac{1+x^{n+1}}{1+x^n}\Bigr)^{x^n}\Bigr)$
negative_passages.docid: 54830
negative_passages.text: Find the limit $\lim\limits_{x\to\infty} f(x)= \lim\limits_{x \to \infty} \left(\frac{x}{x+1}\right)^x$
negative_passages.docid: 101687
negative_passages.text: $ \lim_{x\to o} \frac{(1+x)^{\frac1x}-e+\frac{ex}{2}}{ex^2} $
negative_passages.docid: 117370
negative_passages.text: $\lim_{n\to\infty} \left(1+\frac{2}{n}\right)^{n^2} e^{-2n}$
negative_passages.docid: 44060
negative_passages.text: If $\lim_{x \to +\infty} f'(x) = L$, then $\lim_{x \to \infty} \frac {f(x)}{x} = L$
negative_passages.docid: 106142
negative_passages.text: Why does L'Hopital's rule fail in calculating $\lim_{x \to \infty} \frac{x}{x+\sin(x)}$?
negative_passages.docid: 122485
negative_passages.text: Limit of $f(x+\sqrt x)-f(x)$ as $x \to\infty$ if $|f'(x)|\le 1/x$ for $x>1$
negative_passages.docid: 138169
negative_passages.text: Finding $\lim\limits_{n \to \infty }n\int_{0}^{1}\frac{x^{n}}{1+x+x^{n}}dx$