query: Prove $\lim_{\epsilon \to 0^+}\frac{\mathbb{E}(X^\epsilon)-1}{\epsilon}=\mathbb{E}(\log X)$
positive_passages.docid: 149792
positive_passages.text: Show that $\lim_{p \to 0} \mathbb {E} [(X^p-1)/p ] = \mathbb{E} [\log X]$
negative_passages.docid: 79024
negative_passages.text: the derivation of E(X|X)
negative_passages.docid: 74919
negative_passages.text: Finding limit of function $\lim_{x\to 0}\left(\frac{(1+x)^\frac1x}{e}\right)^\frac1x$
negative_passages.docid: 36417
negative_passages.text: Why does $\mathbb{E}(\frac{X_1+...+X_n}{n})=\mathbb{E}(X)$?
negative_passages.docid: 1840
negative_passages.text: How can I prove that $\log^k(n) = O(n^\epsilon)$?
negative_passages.docid: 71743
negative_passages.text: $\lim (1+\frac{1}{n+1})^n = e$
negative_passages.docid: 108917
negative_passages.text: Use $\delta-\epsilon$ to show that $\lim_{n\to\infty} a^{\frac{1}{n}} = 1$?
negative_passages.docid: 37489
negative_passages.text: Show that $ \lim_{(x,y) \to 0} \frac {|x|^ \alpha |y|^ \beta} {|x|^ \gamma + |y|^ \delta} \text {exists} \iff \alpha/\gamma + \beta/\delta > 1.$
negative_passages.docid: 26226
negative_passages.text: Proving $\lim \limits_{n\to +\infty } \left(1+\frac{x}{n}\right)^n=\text{e}^x$.
negative_passages.docid: 93408
negative_passages.text: Trying to show that $\ln(x) = \lim_{n\to\infty} n(x^{1/n} -1)$
negative_passages.docid: 152860
negative_passages.text: How to evalute $\int_{0}^{1}\frac{x\log x}{\log(1-x)}dx$
negative_passages.docid: 60831
negative_passages.text: Need hint for $\lim_{x\to 0} \frac{(x+1)^\frac{1}{x}-e}{x}$
negative_passages.docid: 52943
negative_passages.text: How to show $\lim_{\epsilon \rightarrow 0} \frac{\epsilon}{x^2+\epsilon ^2} = \pi \delta (x)$?
negative_passages.docid: 147705
negative_passages.text: Show that $\mathbb{E}(T) = \sum\limits^\infty_{k=1}\mathbb{P}(T \geq k)$ for $T$ nonnegative integer valued and $E[T] < \infty$
negative_passages.docid: 158153
negative_passages.text: Prove: $ \lim_{n\rightarrow\infty} x ^ {\left(\frac 1 n\right)} = 1 $
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: 100387
negative_passages.text: Using $\epsilon-\delta$ to prove that a limit is not a specific number