query: Argue that the impromper integral $\int_1^\infty \frac{1-e^{-2x^2}}{x^2}$ for $x \neq 0$ is convergent
positive_passages.docid: 25010
positive_passages.text: Argue that there exists a continuous function $g: \mathbb{R} \rightarrow \mathbb{R}$ which satisfies $g(x) = \frac{1-e^{-2x^2}}{x^2}$ for $x \neq 0$
negative_passages.docid: 142854
negative_passages.text: Convergence of Integrals - A Problem
negative_passages.docid: 119410
negative_passages.text: Solution of $\int_0^\infty\frac{\ln(1+{x^2})}{1+{x^2}}$
negative_passages.docid: 69808
negative_passages.text: For which values of $\alpha$ and $\beta$ does the integral $\int\limits_2^{\infty}\frac{dx}{x^{\alpha}\ln^{\beta}x}$ converge?
negative_passages.docid: 147662
negative_passages.text: For what values $s$ does $\int_{0}^{\infty} \frac{\sin x}{x^s}dx$ converge?
negative_passages.docid: 121736
negative_passages.text: An improper integral : $\int_{0}^\infty {\ln(a^2+x^2)\over{b^2+x^2}}dx$
negative_passages.docid: 157762
negative_passages.text: Showing $f_n(x):=\frac{x}{1+n^2x^2}$ uniformly convergent in $\mathbb R$ using $\epsilon-n_0$
negative_passages.docid: 10675
negative_passages.text: Proving that $\frac{1}{2\pi}\int_{0}^{2\pi}|f(re^{it})|^2dt=\sum_{n=0}^{\infty}|a_n|^2r^{2n}$
negative_passages.docid: 70867
negative_passages.text: Is $\sum_{n=1}^\infty\frac{(-1)^n}{n\log^2(n+1)}$ absolutely convergent?
negative_passages.docid: 35435
negative_passages.text: For what values of $\alpha$, does this integral converge?
negative_passages.docid: 45205
negative_passages.text: Showing that $\int_0^\infty x^{-x} \mathrm{d}x \leq 2$.
negative_passages.docid: 61133
negative_passages.text: Show that $\int|f(x)|dx=\int_0^\infty m(E_\alpha)d\alpha$
negative_passages.docid: 110394
negative_passages.text: For which values this integral converge?
negative_passages.docid: 112951
negative_passages.text: Improper integral $\sin(x)/x $ converges absolutely, conditionaly or diverges?
negative_passages.docid: 48997
negative_passages.text: Self-Contained Proof that $\sum\limits_{n=1}^{\infty} \frac1{n^p}$ Converges for $p > 1$
negative_passages.docid: 133451
negative_passages.text: To show that ${x_n}$ is convergent where $|x_{n+1} - x_n|< \frac{1}{n^2}$
negative_passages.docid: 149055
negative_passages.text: Uniform convergence of $\sum\limits_{k=1}^{\infty}\dfrac{kf(x^2)}{1+k^3f(x^2)^2}$