query: Find $\|T\|_{\ell^\infty \rightarrow \ell^2}$
positive_passages.docid: 155974
positive_passages.text: Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
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: 136450
negative_passages.text: Compute $\lim_{x \rightarrow +\infty} \frac{[\int^x_0 e^{y^{2}} dy]^2}{\int^x_0 e^{2y^{2}}dy}$
negative_passages.docid: 73865
negative_passages.text: Find $\lim_{n\to\infty}n\left(\sum_{i=1}^{n}\dfrac{1}{(n+i)^2}\right)$
negative_passages.docid: 44095
negative_passages.text: Prove that $\lim_{x\to \infty}\left(x-\ln\cosh x\right)=\ln 2$
negative_passages.docid: 140574
negative_passages.text: Find $\lim_{n\to \infty} \int_0^1 nx^n e^{x^2} dx$
negative_passages.docid: 569
negative_passages.text: How do I determine $\lim_{x\to\infty} \left[x - x^{2} \log\left(1 + 1/x\right)\right]$?
negative_passages.docid: 63023
negative_passages.text: Evaluation of $\lim_{x\rightarrow \infty}\sqrt{x^2+x+1} -\lfloor \sqrt{x^2+x+1 }\rfloor\;,$
negative_passages.docid: 95718
negative_passages.text: Computing $ \lim_{n\rightarrow \infty}\left(\frac{1^n+2^n+\cdots \cdots +n^n}{n^n}\right)$
negative_passages.docid: 9223
negative_passages.text: Finding $\iiint_K (x^2 -z^2)\, dx\, dy \,dz$
negative_passages.docid: 146839
negative_passages.text: Orthogonal Projection onto the $ {L}_{\infty} $ Unit Ball
negative_passages.docid: 144403
negative_passages.text: Limit $\lim_{x\rightarrow +\infty}\sqrt{x}e^{-x}\left(\sum_{k=1}^{\infty}\frac{x^{k}}{k!\sqrt{k}}\right)$
negative_passages.docid: 45537
negative_passages.text: Finding the limit $\lim_{x\rightarrow \infty} \sqrt[3]{x+1}-\sqrt[3]{x}$
negative_passages.docid: 44737
negative_passages.text: $ \int_{-\infty}^{\infty} x^4 e^{-ax^2} dx$
negative_passages.docid: 145668
negative_passages.text: Subspaces of $\ell^{2}$ and $\ell^{\infty}$ which are not closed?
negative_passages.docid: 10093
negative_passages.text: $\lim_{x\to \infty}e^{-x^2}\int_x^{x+1/x}e^{t^2}dt$
negative_passages.docid: 95921
negative_passages.text: Question about $\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}$