query: How do i evaluate this limit :$\lim_{x \to 0} \frac{e^x-x-1}{x²}$ without using Taylor expansion
positive_passages.docid: 65213
positive_passages.text: How to find $\lim\limits_{x\to0}\frac{e^x-1-x}{x^2}$ without using l'Hopital's rule nor any series expansion?
negative_passages.docid: 5157
negative_passages.text: How to evaluate $ \lim_{(x,y)\to(0,0)}\frac{y^2\sin^2x}{x^4+y^4} $
negative_passages.docid: 117542
negative_passages.text: Finding the limit $\displaystyle\lim_{x\to 0+} \left(\frac{\sin x}x\right)^{1/{x^2}}$
negative_passages.docid: 111929
negative_passages.text: Find the limit: $\lim_\limits{x\to 0}{\frac{\left(1+x\right)^{1/x}-e}{x}}$
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: 101536
negative_passages.text: Difficult limit evaluation: $\lim_{x\to\infty}(\sqrt{x^2+4x} - x)$
negative_passages.docid: 19263
negative_passages.text: Limit as $x\to 0$ of $\frac{(1+x)^{1/x}-e}{x}$
negative_passages.docid: 88782
negative_passages.text: Finding the limit of $x_1=0 , x_{n+1}=\frac{1}{1+x_n}$
negative_passages.docid: 27717
negative_passages.text: Compute $\lim_{x\to\infty}x\;\left[\left(1+\frac{1}{x}\right)^x-e\right]$
negative_passages.docid: 78877
negative_passages.text: Limit: $\lim\limits_{x\to0}\frac{e^x-e^{\sin x}}{x-\sin x}$
negative_passages.docid: 5974
negative_passages.text: Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$
negative_passages.docid: 36648
negative_passages.text: The limit of $((1+x)^{1/x} - e+ ex/2)/x^2$ as $x\to 0$
negative_passages.docid: 100893
negative_passages.text: Determine $\lim_{x \to 0}{\frac{x-\sin{x}}{x^3}}=\frac{1}{6}$, without L'Hospital or Taylor
negative_passages.docid: 22686
negative_passages.text: Show $\lim_{h\to 0} \frac{(a^h-1)}{h}$ exists without l'Hôpital or even referencing $e$ or natural log
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: 119469
negative_passages.text: Find the limit of $\lim\limits_{(x,y)\to (0,0)} \frac{x^2y^2}{x^2y^2+(x-y)^2}$
negative_passages.docid: 53719
negative_passages.text: Evaluate $\lim_{x \to 0} \left(\frac{1}{\ln(1+x)} + \frac{1}{\ln(1-x)}\right)$