Question Number 138742 by mnjuly1970 last updated on 17/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:……..\:{nice}\:\:\:….\:\:\:{calculus}… \\ $$$$\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{x}^{{e}^{\pi} −\mathrm{1}} −{x}^{{e}^{\gamma} −\mathrm{1}} }{{ln}\left(\sqrt[{\mathrm{3}}]{{x}}\:\right)}{dx}\overset{?} {=}\mathrm{3}\left(\pi−\gamma\right) \\ $$ Answered by…
Question Number 7668 by 314159 last updated on 08/Sep/16 Commented by Yozzia last updated on 08/Sep/16 $${Suppose}\:{a}+{b}={c},\:{with}\:{a},{b},{c}>\mathrm{0}. \\ $$$${Let}\:{n}=\frac{{a}}{\mathrm{1}+{a}}+\frac{{b}}{\mathrm{1}+{b}}−\frac{{c}}{\mathrm{1}+{c}}. \\ $$$${n}=\frac{{a}}{\mathrm{1}+{a}}+\frac{{b}}{\mathrm{1}+{b}}−\frac{{a}+{b}}{\mathrm{1}+{a}+{b}} \\ $$$${n}=\frac{{a}}{\mathrm{1}+{a}}−\frac{{a}}{\mathrm{1}+{a}+{b}}+\frac{{b}}{\mathrm{1}+{b}}−\frac{{b}}{\mathrm{1}+{a}+{b}} \\ $$$${n}={a}\left(\frac{\mathrm{1}}{\mathrm{1}+{a}}−\frac{\mathrm{1}}{\mathrm{1}+{a}+{b}}\right)+{b}\left(\frac{\mathrm{1}}{\mathrm{1}+{b}}−\frac{\mathrm{1}}{\mathrm{1}+{a}+{b}}\right)…
Question Number 73202 by MJS last updated on 08/Nov/19 $$\int\frac{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{1}+\mathrm{2}{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}^{\mathrm{2}} −{x}+\left({x}−\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{dx}=? \\ $$$$\int\frac{{dx}}{{x}\sqrt{{x}+\mathrm{1}}\sqrt{\left(\mathrm{1}−{x}\right)^{\mathrm{3}} }}=? \\ $$ Commented by mathmax by abdo last…
Question Number 7667 by upendrakishor99@gmail.com last updated on 08/Sep/16 $$\underset{{x}\rightarrow\alpha} {\mathrm{lim}}\left[{x}−{x}^{\mathrm{2}} \mathrm{log}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\right] \\ $$ Answered by FilupSmith last updated on 08/Sep/16 $$=\alpha−\alpha^{\mathrm{2}} \mathrm{log}\left(\mathrm{1}+\frac{\mathrm{1}}{\alpha}\right) \\ $$…
Question Number 73203 by Tanmay chaudhury last updated on 08/Nov/19 Commented by kaivan.ahmadi last updated on 08/Nov/19 $${xsin}\frac{\mathrm{1}}{{x}}=\mathrm{1}\Rightarrow{sin}\frac{\mathrm{1}}{{x}}=\frac{\mathrm{1}}{{x}}\Rightarrow\frac{\mathrm{1}}{{x}}=\mathrm{0}\Rightarrow{there}\:{is}\:{no}\:{root} \\ $$$${so}\:{A}\:{has}\:{exactly}\:{one}\:{element},\:{A}=\left\{\mathrm{0}\right\} \\ $$ Terms of Service…
Question Number 73200 by aliesam last updated on 07/Nov/19 $${if}\:\: \\ $$$$ \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}^{+} } {{lim}f}\left({x}\right)=+\infty \\ $$$$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{−} } {{lim}f}\left({x}\right)=+\infty \\ $$$$ \\…
Question Number 7665 by upendrakishor99@gmail.com last updated on 08/Sep/16 $$\frac{{d}}{{dx}}\sqrt{{x}^{\mathrm{2}} −\mathrm{4}} \\ $$ Answered by Rasheed Soomro last updated on 08/Sep/16 $$\frac{{d}}{{dx}}\left({x}^{\mathrm{2}} −\mathrm{4}\right)^{\mathrm{1}/\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{2}}\left({x}^{\mathrm{2}} −\mathrm{4}\right)^{\left(\mathrm{1}/\mathrm{2}\right)−\mathrm{1}}…
Question Number 138733 by mnjuly1970 last updated on 17/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{mathematical}\:….{analysis}….. \\ $$$$\:\:{suppose}\:\:\:\:{f}\::\left[{a}\:,\:{b}\right]\rightarrow\mathbb{R}\:{is}\:{a}\:{function} \\ $$$$\:\:\:{and}\:\:\:\alpha:\left[{a}\:,\:{b}\right]\overset{\alpha\nearrow} {\rightarrow}\mathbb{R}\:\left(\alpha\:{is}\:{an}\:{increasing}\:{function}\right. \\ $$$$\left.\:{on}\:\left[{a}\:,\:{b}\right]\right)\:\:{meanwhile}\:\alpha\:{is}\:{continuous}\:{at}\:{y}_{\mathrm{0}} \: \\ $$$$\:\:{where}\:\:\:{a}\leqslant{y}_{\mathrm{0}} \leqslant{b}\:\:.\:{defining}\: \\ $$$$\:\:\:{f}\left({x}\right)=\begin{cases}{\:\mathrm{1}\:\:\:\:\:\:\:\:\:{x}={y}_{\mathrm{0}} }\\{\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:{x}\neq{y}_{\mathrm{0}} }\end{cases}…
Question Number 7663 by malwaan last updated on 07/Sep/16 $$\int{tan}\sqrt{{x}\:}{dx} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 138735 by SanyamJoshi last updated on 17/Apr/21 Answered by Ajaypareek last updated on 17/Apr/21 $$\mathrm{1} \\ $$ Answered by bramlexs22 last updated on…