query: How do I prove this limit does not exist: $\lim_{x\rightarrow 0} \frac{e^{1/x} - 1}{e^{1/x} + 1} $ i ve a doubt
positive_passages.docid: 155188
positive_passages.text: How do I prove this limit does not exist: $\lim_{x\rightarrow 0} \frac{e^{1/x} - 1}{e^{1/x} + 1} $
negative_passages.docid: 121606
negative_passages.text: How do I prove that the limit of the sequence exists: $a_n = \frac1n +\frac 1{n+1} + \frac1{n+2} + \dots + \frac1{2n}$?
negative_passages.docid: 78877
negative_passages.text: Limit: $\lim\limits_{x\to0}\frac{e^x-e^{\sin x}}{x-\sin x}$
negative_passages.docid: 104996
negative_passages.text: Limit of $\lim_{n\rightarrow \infty} \sum^{n}_{i=1} \frac{1}{\sqrt {n^2 +i} }$
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: 75567
negative_passages.text: Find $\lim_{n \to \infty} \left[\frac{(n+1)^{n + 1}}{n^n} - \frac{n^{n}}{(n-1)^{n-1}} \right]$ (a question asked at trivia)
negative_passages.docid: 80440
negative_passages.text: Limit of $(x_n)$ with $0<x_1<1$ and $x_{n + 1} = x_n - x_n^{n + 1}$
negative_passages.docid: 53918
negative_passages.text: whats the proof for $\lim_{x → 0} [(a_1^x + a_2^x + .....+ a_n^x)/n]^{1/x} = (a_1.a_2....a_n)^{1/n}$
negative_passages.docid: 80720
negative_passages.text: What paths to choose to prove that $\lim_{(x,y) \to (0,0)}\frac{xy^2}{x^2 - y^2}$ does not exist?
negative_passages.docid: 115132
negative_passages.text: Give an example about limits: $\lim\limits_{x\to0}f(x^{2})$ exists but $\lim\limits_{x\to0}f(x)$ does not.
negative_passages.docid: 67894
negative_passages.text: $\epsilon$-$\delta$ proof that $\lim\limits_{x \to 1} \frac{1}{x} = 1$.
negative_passages.docid: 33337
negative_passages.text: $\int_{0}^{\infty} f(x) \,dx$ exists. Then $\lim_{x\rightarrow \infty} f(x) $ must exist and is $0$. A rigorous proof?
negative_passages.docid: 2167
negative_passages.text: Find the limit $\lim\limits_{x\to \infty}(e^{-x}+2\cos3x)$, or show that it does not exist.
negative_passages.docid: 115028
negative_passages.text: If $e=\lim\limits_{x\to \infty} (1+x^{-1})^x$, why doesn't $e=1$?
negative_passages.docid: 6396
negative_passages.text: If two limits don't exist, are we sure the limit of sum doesn't exist?
negative_passages.docid: 112481
negative_passages.text: Given $a_{n+1} = \frac{{a_n}}{\sin({a_n})}$ with $0 < a_1 < \frac{\pi}{2}$. Show that the limit $\lim_{n\rightarrow\infty}{a_n}$ exists and find it.
negative_passages.docid: 33495
negative_passages.text: A limit problem about $a_{n+1}=a_n+\frac{n}{a_n}$