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 Feb5 accepted Calculate this limit $\lim_{n\to \infty } \, \frac{(-1)^n \left(n^2 \sin (n)+2 n\right)}{{n^2}+3}$ Feb4 accepted Evaluating $\int{\frac{1}{\sqrt{x^2-1}(x^2+1)}dx}$ Feb3 accepted Evaluate $\int\sqrt[5]{\frac{x+5}{x-5}}\,\mathrm dx$ Jan27 accepted Limit find $f(x)$ $\lim_{x\to1}\frac{f(x)\cos{\frac{\pi x}{2}}}{\sqrt[3]x-1}=3$ Jan27 accepted Series proof $\sum_1^\infty|a_n|<\infty$ then show that $\sum_1^\infty{a_n^2}<\infty$ Jan26 accepted Limit evaluation $\lim_{x\to2}\frac{\sqrt{12-x^3}-\sqrt[3]{x^2+4}}{x^2-4}$ Jan23 accepted Convergence of $\sum_{n=1}^\infty{\frac{\ln({3n^2 +4n+5})}{n^{4/3}}}$ Jan23 accepted $\sum_1^\infty{\frac{(-1)^n}{\ln{(2\cosh{n})}}}$ convergence Jan21 accepted Series convergence: $\sum_{n=1}^\infty\frac{\sin{\frac{n\pi}{2}}}{n^{2/3}}$ Jan16 accepted Limit of this recursive sequence and convergence Jan16 accepted Sequence limit and monotony of $a_{n+1}=\sqrt{4a_n+3},a_1=5$ Jan15 accepted Proof definite integral $\int_α^{π/2-α}f(\tan{x})dx=\frac{\pi}{2}-α$ Dec14 accepted Area within $x=0$ $y=x$ and $e^{-x}$ Dec14 accepted $y=e^{-x}$ and $y=x$ point of intersection Dec8 accepted How to show this $\lim_{n\rightarrow\infty} {\sqrt[n]{1+n^2}} =1$ Dec8 accepted Series convergence of $\sum_1^\infty\frac{(n!)^2+(2n)^n}{n^{2n}}$ Dec1 accepted Roots of $x^4 -6x^3 +x^2+10x +1=0$ Nov28 accepted Point of inflection and third derivative Nov10 accepted $\sum_1^\infty (-1)^n \left(1 + \frac{2}{n^2}\right)^{n^2}$ series diverge Nov10 accepted Prove that $\sum_{n=1}^{\infty}\frac{1}{n(n+1)\cdots(n+a)}=\frac{1}{aa!}$