query: Show that $ \lim_{x\rightarrow x_{0}}u\left( x\right) $ exists and $u$ is harmonic in $\Omega$
positive_passages.docid: 18207
positive_passages.text: Removable singularity for harmonic functions
negative_passages.docid: 97522
negative_passages.text: Calculating a limit with Harmonic number
negative_passages.docid: 45806
negative_passages.text: Finding $\lim\limits_{n \rightarrow \infty}\left(\int_0^1(f(x))^n\,\mathrm dx\right)^\frac{1}{n}$ for continuous $f:[0,1]\to[0,\infty)$
negative_passages.docid: 13561
negative_passages.text: Show: $E(|X|)\leqslant\liminf_{n\to\infty} E(|X_n|)$
negative_passages.docid: 60498
negative_passages.text: Prove that $\lim_{(x,y)\rightarrow(0,0)} \frac{|x|^{a}|y|^{b}}{|x|^{c} + |y|^{d}}$ does not exist
negative_passages.docid: 12301
negative_passages.text: Show that $\lim_{n \rightarrow \infty} \sqrt[n]{a} =1$
negative_passages.docid: 34127
negative_passages.text: Prove $\lim_{x \rightarrow 0} \frac {\sin(x)}{x} = 1$ with the epsilon-delta definition of limit.
negative_passages.docid: 1371
negative_passages.text: Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
negative_passages.docid: 135999
negative_passages.text: One sided limit of an increasing function defined on an open interval
negative_passages.docid: 128761
negative_passages.text: An $\varepsilon-\delta$ proof of $\lim_{x\rightarrow c} (2x^ 2 − 3x + 4) = 2c ^2 − 3c + 4$.
negative_passages.docid: 101778
negative_passages.text: Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$
negative_passages.docid: 94910
negative_passages.text: How does one show that $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$ converges?
negative_passages.docid: 156478
negative_passages.text: Prove that $\lim_{n\rightarrow\infty}\frac{x_1^2+x_2^2+\cdots+x_n^2}{n^2}=0$
negative_passages.docid: 6620
negative_passages.text: If $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x)) =L<\infty$, does $\lim\limits_{x\rightarrow\infty} f(x) $ exist?
negative_passages.docid: 149822
negative_passages.text: If $\omega \in \Omega^q(M)$, and $(\omega|_{U})_p = 0$, is $\omega_p = 0$?
negative_passages.docid: 94066
negative_passages.text: Prove that: {$f_n$} converges unifromly to $f$ on $E$ as $n \rightarrow \infty$ if and only if $\lim_{n\rightarrow \infty} ||f_n-f||_u = 0$
negative_passages.docid: 37055
negative_passages.text: Show that $\lim _{r \to 0} \|T_rf−f\|_{L_p} =0.$