query: Evaluate $ \lim _{x \to 0} \left[{\frac{x^2}{\sin x \tan x}} \right]$ where $[\cdot]$ denotes the greatest integer function.
positive_passages.docid: 19791
positive_passages.text: Calculating $\lim_{x\to0} \left\lfloor\frac{x^2}{\sin x \tan x}\right\rfloor$
negative_passages.docid: 71891
negative_passages.text: $\lim_{x \to 0} f(x)=\frac{\tan 3x}{\tan 2x}$ without L'Hospital
negative_passages.docid: 38271
negative_passages.text: Which is the easiest way to evaluate $\int \limits_{0}^{\pi/2} (\sqrt{\tan x} +\sqrt{\cot x})$?
negative_passages.docid: 22709
negative_passages.text: Show that $\lim_{x\to \frac{\pi}{2}} \frac{1}{\big(x-\frac{\pi}{2}\big)}+{\tan(x)}=0$.
negative_passages.docid: 126749
negative_passages.text: Evaluate $\lim_{x \rightarrow 0} x^x$
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: 569
negative_passages.text: How do I determine $\lim_{x\to\infty} \left[x - x^{2} \log\left(1 + 1/x\right)\right]$?
negative_passages.docid: 67429
negative_passages.text: Solve $\lim_{x\to0}{\frac{x^2\cdot\sin\frac{1}{x}}{\sin x}}$
negative_passages.docid: 23217
negative_passages.text: About $\lim \left(1+\frac {x}{n}\right)^n$
negative_passages.docid: 98367
negative_passages.text: Limit of $\left(\frac{n^2+2}{2n^2+1}\right)^{n^2}$
negative_passages.docid: 136738
negative_passages.text: Does the limit $\lim _{x\to 0} \frac 1x \int_0^x \left|\cos \frac 1t \right| dt$ exists?
negative_passages.docid: 41659
negative_passages.text: Limit as $x\to 0$ of $x\sin(1/x)$
negative_passages.docid: 156141
negative_passages.text: Limit of $\left(1-\frac{1}{n^2}\right)^n$
negative_passages.docid: 49489
negative_passages.text: Compute $\lim_{n\to\infty} \int_{0}^{\pi/4}\tan^n x \ dx$
negative_passages.docid: 46654
negative_passages.text: Using the Squeeze Theorem on $\lim_{x\to 0}\frac{\sin^2x}{x^2}$
negative_passages.docid: 128456
negative_passages.text: Evaluating $\lim_{x\to0}\left(\frac{1+x2^x}{1+x3^x}\right)^\frac1{x^2}$
negative_passages.docid: 91290
negative_passages.text: Evaluating $\lim_{n \to \infty} \int_{0}^{\pi} \frac{\sin x}{1+\cos ^2(nx)} dx$