Question Number 1100 by malwaan last updated on 13/Jun/15 $${compare}\:{log}_{\mathrm{2}} \mathrm{3}\:{and}\:{log}_{\mathrm{3}} \mathrm{5} \\ $$ Answered by 123456 last updated on 13/Jun/15 $$\mathrm{log}_{\mathrm{2}} \mathrm{3}={x}\Leftrightarrow\mathrm{2}^{{x}} =\mathrm{3}\: \\…
Question Number 1096 by rpatle69@gmail.com last updated on 13/Jun/15 $${solve}\:{this} \\ $$$$\left({tanA}+{secA}−\mathrm{1}\right)/\left({tanA}−{secA}+\mathrm{1}\right) \\ $$$$=\left(\mathrm{1}+{sinA}\right)/{cosA} \\ $$$$ \\ $$ Answered by prakash jain last updated on…
Question Number 1093 by 123456 last updated on 12/Jun/15 $$\mathrm{can}\:\mathrm{a}\:\mathrm{function}\:{f}\:\mathrm{be}\:\mathrm{such}\:\mathrm{that}\:\mathrm{for}\:{a}\in\mathbb{R} \\ $$$${f}:\mathrm{X}/\left\{{a}\right\}\rightarrow\mathbb{R},\left({a}−\delta,{a}+\delta\right)\in\mathrm{X},\mathrm{X}\subset\mathbb{R},\delta\in\mathbb{R},\delta>\mathrm{0} \\ $$$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:{f}\left({x}\right)=\infty \\ $$$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:\mid{f}'\left({x}\right)\mid<\infty \\ $$ Answered by prakash jain last…
Question Number 66629 by Sayantan chakraborty last updated on 17/Aug/19 Commented by Sayantan chakraborty last updated on 09/Sep/19 $$\mathrm{Can}\:\mathrm{anybody}\:\mathrm{solve}\:\mathrm{it}??? \\ $$ Terms of Service Privacy…
Question Number 66627 by behi83417@gmail.com last updated on 17/Aug/19 Commented by behi83417@gmail.com last updated on 17/Aug/19 $$\mathrm{reposted}!\:\:\mathrm{Q}#\mathrm{62227} \\ $$ Commented by mathmax by abdo last…
Question Number 132162 by Dwaipayan Shikari last updated on 11/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({n}\right)}{{n}^{\mathrm{2}} } \\ $$ Answered by mnjuly1970 last updated on 11/Feb/21 $$\frac{\mathrm{1}}{\mathrm{2}{i}}\left[{li}_{\mathrm{2}} \left({e}^{{i}}…
Question Number 1088 by 112358 last updated on 10/Jun/15 $${Solve}\:{the}\:{following}\:{integral} \\ $$$${equation}\:{for}\:{f}\left({x}\right): \\ $$$$\int_{\mathrm{0}} ^{\:{x}} {f}\left({t}\right){dt}=\mathrm{3}{f}\left({x}\right)+{k} \\ $$$${where}\:{k}\:{is}\:{a}\:{constant}.\: \\ $$ Answered by prakash jain last…
Question Number 66620 by Mohamed Amine Bouguezzoul last updated on 18/Aug/19 $${find}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{I}_{{n}} \\ $$$${I}_{{n}} =\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{\left(\mathrm{1}+\mathrm{coth}\:\left({nx}\right)\right)^{{n}} }\:,{n}\geqslant\mathrm{1} \\ $$$$ \\ $$ Commented by…
Question Number 1085 by 123456 last updated on 10/Jun/15 $$\mathrm{I}=\underset{\mathrm{0}} {\overset{\pi} {\int}}\frac{{x}\left(\pi−{x}\right)}{\mathrm{sin}\:{x}}{dx} \\ $$ Commented by 123456 last updated on 10/Jun/15 $${f}\left({x}\right)=\frac{{x}\left(\pi−{x}\right)}{\mathrm{sin}\:{x}} \\ $$$${f}\left(\mathrm{0}^{+} \right)\overset{?}…
Question Number 66621 by lalitchand last updated on 17/Aug/19 Commented by lalitchand last updated on 17/Aug/19 $$\mathrm{8}\:\mathrm{iii} \\ $$ Commented by mr W last updated…