query: Show that $\lim_{n \to \infty} \frac{1}{\sqrt{n}} \int_{[0,1]^n} |x|dx= \frac{1}{\sqrt3}\space $
positive_passages.docid: 19729
positive_passages.text: An infinite dimensional limit
negative_passages.docid: 35325
negative_passages.text: Prove that $\lim_{n\to\infty}\frac1{n}\int_0^{n}xf(x)dx=0$.
negative_passages.docid: 97256
negative_passages.text: For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
negative_passages.docid: 101630
negative_passages.text: Limit $\lim_{n\to\infty}\sqrt n(\sqrt[n]x-1)$
negative_passages.docid: 105527
negative_passages.text: Show that $\lim_{r\to 0} \frac{1}{r^2}\int_{C_{r}}f(z)dz = 2 \pi i\frac{\partial f}{\partial \bar{z}}(z_0)$
negative_passages.docid: 72693
negative_passages.text: Prove: $\lim_{x\to\infty}x^{2/3}((x+1)^{1/3}-x^{1/3})=1/3$
negative_passages.docid: 41434
negative_passages.text: Show that: $\lim \limits_{n \rightarrow+\infty} \int_{0}^{1}{f(x^n)dx}=f(0)$
negative_passages.docid: 151149
negative_passages.text: $\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
negative_passages.docid: 113141
negative_passages.text: Prove that $\lim_{n \to \infty}\bigg[\int_0^1f(t)^n \text{dt}\bigg]^{1/n}=M$
negative_passages.docid: 966
negative_passages.text: Show that $\lim_{n\rightarrow \infty} \sqrt[n]{c_1^n+c_2^n+\ldots+c_m^n} = \max\{c_1,c_2,\ldots,c_m\}$
negative_passages.docid: 120777
negative_passages.text: How to formally prove that if $\lim \limits_{n \to \infty}a_n=\infty$, then $\lim \limits_{n \to \infty}\frac{1}{a_n}=0$.
negative_passages.docid: 136297
negative_passages.text: Evaluate $\lim_{x \to 1} \frac{\sqrt[3]{x} -1}{\sqrt{x} -1}$
negative_passages.docid: 19631
negative_passages.text: Finding $\lim_{n\to \infty}\sqrt n \int_0^1 \frac{\,dx}{(1+x^2)^n}$
negative_passages.docid: 11489
negative_passages.text: Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$
negative_passages.docid: 30160
negative_passages.text: How to show that $\lim_{n \to +\infty} n^{\frac{1}{n}} = 1$?
negative_passages.docid: 4003
negative_passages.text: Limit of : $\lim\limits_{n\to\infty}{(\sqrt[3]{n+1}-\sqrt[3]{n})}$.
negative_passages.docid: 16775
negative_passages.text: Showing that $\int_{0}^{\infty} \frac{dx}{1 + x^2} = 2 \int_0^1 \frac{dx}{1 + x^2}$