query: Limit involving exponentials of $\arcsin(x)$ and $\arctan(x)$
positive_passages.docid: 15888
positive_passages.text: How to calculate limit without L'Hopital
negative_passages.docid: 103757
negative_passages.text: how can I prove that $\frac{\arctan x}{x }< 1$?
negative_passages.docid: 32742
negative_passages.text: The limit of $\frac{|A_n|}{n^2}$
negative_passages.docid: 117370
negative_passages.text: $\lim_{n\to\infty} \left(1+\frac{2}{n}\right)^{n^2} e^{-2n}$
negative_passages.docid: 74684
negative_passages.text: $\lim_{x \to 0} {1-x\cot x\over x^2}$
negative_passages.docid: 31889
negative_passages.text: The limit as $n$ approaches infinity of $n(a^{1/n}-1)$
negative_passages.docid: 36888
negative_passages.text: How to prove that the limit of an $n$-gon is a circle?
negative_passages.docid: 113781
negative_passages.text: How can I calculate $\lim_{x\to 0} \frac{\arctan(x)-\arcsin(x)}{x^3}$ without L'Hôpital?
negative_passages.docid: 95673
negative_passages.text: General formula for $\sin\left(k\arcsin (x)\right)$
negative_passages.docid: 43829
negative_passages.text: Limit of $h_n(x)=x^{1+\frac{1}{2n-1}}$
negative_passages.docid: 155539
negative_passages.text: Evaluating the limit $\lim_{x \to 0+}\left(\frac{1}{x}-\frac{1}{\arctan(x)}\right)$
negative_passages.docid: 71796
negative_passages.text: Proving $\rm \frac i 2 \ln\frac {x+i}{x-i}=\arctan x$ .
negative_passages.docid: 158447
negative_passages.text: Limit as $(x,y)$ approaches $(0,0)$ of $(1+x^2+y^2)^{\frac{1}{x^2+y^2+xy^2}}$
negative_passages.docid: 89251
negative_passages.text: Limit $\lim\limits_{x\to0}{\frac{\ln{(e+x)}-e^x}{\cos^2{x} -e^x}}$
negative_passages.docid: 24234
negative_passages.text: How to evaluate $\lim_{x\to\infty}\arctan (4/x)/ |\arcsin (-3/x)|$?
negative_passages.docid: 20359
negative_passages.text: Proof of radius of convergence exponential function
negative_passages.docid: 101687
negative_passages.text: $ \lim_{x\to o} \frac{(1+x)^{\frac1x}-e+\frac{ex}{2}}{ex^2} $