query: Calculate $\lim_{x \to a} \frac{\log(x-a)}{\log(e^x-e^a)}$ without using L'Hopital
positive_passages.docid: 146529
positive_passages.text: Finding the limit $ \lim_{x\to a^+} \frac{\cos(x)\ln(x-a)}{\ln(e^x-e^a)} $
negative_passages.docid: 91306
negative_passages.text: Integration of $\frac{1}{\log(x)}$
negative_passages.docid: 135731
negative_passages.text: Is there a way to show that $e^x=\lim_{n\to \infty }\left(1+\frac{x}{n}\right)^n$?
negative_passages.docid: 148170
negative_passages.text: Difficulty in evaluating a limit: $\lim_{x \to \infty} \frac{e^x}{\left(1+\frac{1}{x}\right)^{x^2}}$
negative_passages.docid: 85531
negative_passages.text: Calculate $\lim_{x\to 0}\frac{1}{x^{\sin(x)}}$
negative_passages.docid: 70086
negative_passages.text: Limit without l'Hopital or Taylor series: $\lim\limits_{x \to 0} \frac{x\cos x- \sin x}{x^3}$
negative_passages.docid: 102013
negative_passages.text: The derivative of $e^x$ using the definition of derivative as a limit and the definition $e^x = \lim_{n\to\infty}(1+x/n)^n$, without L'Hôpital's rule
negative_passages.docid: 95991
negative_passages.text: How to solve $\lim_{x \rightarrow 0} {\frac{(1+x)^a-1}{x}}$?
negative_passages.docid: 70742
negative_passages.text: Evaluate $\lim_{x\rightarrow 0} \frac{\sin (6x)}{\sin(2x)}$ without L'Hopital
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: 32853
negative_passages.text: Computing $\lim_{A\to\infty} \frac{1}{A} \int\limits_1^A \! A^{\frac{1}{x}} \, \mathrm{d}x.$
negative_passages.docid: 113765
negative_passages.text: $\lim_{x\to0} \frac{x-\sin x}{x-\tan x}$ without using L'Hopital
negative_passages.docid: 46990
negative_passages.text: $\lim_{x\to0}\frac{e^x-1-x}{x^2}$ using only rules of algebra of limits.
negative_passages.docid: 118204
negative_passages.text: Finding limit of $\left(1 +\frac1x\right)^x$ without using L'Hôpital's rule.
negative_passages.docid: 51622
negative_passages.text: Evaluating $\lim\limits_{x\rightarrow0}\frac{e^{-1/x^2}}{x}$
negative_passages.docid: 135159
negative_passages.text: Limits using L'Hopital's rule $\lim_{x\to0^+} (x^{x^x-1})$
negative_passages.docid: 30937
negative_passages.text: How do I find $\lim\limits_{x \to 0} x\cot(6x) $ without using L'hopitals rule?