query: Limit of given fraction approaching to zero
positive_passages.docid: 13249
positive_passages.text: Multivariable limit proof: $\lim\limits_{(x,y)\rightarrow (0,0)}\frac{\left|x\right|^a\left|y\right|^b}{\left|x\right|^c + \left|y\right|^d} = 0$
negative_passages.docid: 97747
negative_passages.text: Limit of $\lim\limits_{n\to\infty} (1 + \frac{x_n}{n})^n$
negative_passages.docid: 113336
negative_passages.text: Limit of $(\frac{1}{n^2})^{(\frac{1}{n})}$
negative_passages.docid: 41419
negative_passages.text: Solution of limit $\lim\limits_{x\to 0} \frac {e^{-1/x^2}}{x} $
negative_passages.docid: 74919
negative_passages.text: Finding limit of function $\lim_{x\to 0}\left(\frac{(1+x)^\frac1x}{e}\right)^\frac1x$
negative_passages.docid: 91759
negative_passages.text: Evaluate $\lim_{x \to 0} (x\lfloor\frac{1}{x}\rfloor)$
negative_passages.docid: 155377
negative_passages.text: How can I calculate this limit: $\lim\limits_{x\to 0} x\left\lfloor\frac{1}{x}\right\rfloor$?
negative_passages.docid: 143227
negative_passages.text: Show that: $\lim \limits_{n\to\infty}\frac{x_n-x_{n-1}}{n}=0 $
negative_passages.docid: 60831
negative_passages.text: Need hint for $\lim_{x\to 0} \frac{(x+1)^\frac{1}{x}-e}{x}$
negative_passages.docid: 17069
negative_passages.text: Limit $\lim_{x\to \infty} \frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x+2}+\sqrt{x}-\sqrt{4x+12}}$
negative_passages.docid: 123568
negative_passages.text: Solving limit given a limit
negative_passages.docid: 51212
negative_passages.text: How do I solve $\lim\limits_{x\to\infty} \ \frac{\ln \ x}{x} = 0$?
negative_passages.docid: 94168
negative_passages.text: evaluate the limit as $x$ approaches $0$ of $(\cos x-1)/x$ without l'Hopital's rule
negative_passages.docid: 48716
negative_passages.text: Evaluating the limit of $\lim_{x \to 9} \frac {x-9} {\sqrt{x} - 3}$
negative_passages.docid: 81537
negative_passages.text: Limit: $\lim_{x\to 0}\frac{\tan3x}{\sin2x}$
negative_passages.docid: 44668
negative_passages.text: Limit of $x\left(\left(1 + \frac{1}{x}\right)^x - e\right)$ when $x\to\infty$
negative_passages.docid: 48041
negative_passages.text: Compute the given limit as $x$ approaches $\infty$