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Question Number 128874 by help last updated on 11/Jan/21 Commented by Ritu Jain last updated on 11/Jan/21 $$\mathrm{18} \\ $$ Answered by Olaf last updated…

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Question Number 128806 by LUFFY last updated on 10/Jan/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\left({n}^{\mathrm{2}} +{k}^{\mathrm{2}} \right)}\:=\:?????? \\ $$ Answered by Dwaipayan Shikari last updated on 10/Jan/21 $$\underset{{n}=\mathrm{1}}…

Question Number 128752 by naka3546 last updated on 10/Jan/21 $$\int\:\:\frac{{dx}}{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{12}{x}+\mathrm{9}}\:\:=\:\:\:? \\ $$ Answered by mr W last updated on 10/Jan/21 $$\int\frac{{dx}}{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{12}{x}+\mathrm{9}} \\ $$$$=\int\frac{{dx}}{\mathrm{2}\left({x}+\mathrm{3}\right)^{\mathrm{2}}…

Question Number 128745 by shaker last updated on 10/Jan/21 Answered by liberty last updated on 10/Jan/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\mathrm{mnx}+\frac{\mathrm{n}\left(\mathrm{n}−\mathrm{1}\right)}{\mathrm{2}}\mathrm{m}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} \right)−\left(\mathrm{1}+\mathrm{mnx}+\frac{\mathrm{m}\left(\mathrm{m}−\mathrm{1}\right)}{\mathrm{2}}\mathrm{n}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{2}} }= \\ $$$$\frac{\mathrm{m}^{\mathrm{2}}…