Question Number 68554 by Mikael last updated on 13/Sep/19 Commented by Prithwish sen last updated on 13/Sep/19 $$\mathrm{li}\underset{\mathrm{n}\rightarrow\infty} {\mathrm{m}}\frac{\mathrm{1}}{\mathrm{n}}\left[\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{0}}{\mathrm{n}}}+\:\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{n}}}\:+……+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{n}−\mathrm{1}}{\mathrm{n}}}\right] \\ $$$$=\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}}\underset{\boldsymbol{\mathrm{r}}=\mathrm{0}} {\overset{\boldsymbol{\mathrm{n}}−\mathrm{1}} {\sum}}\:\:\boldsymbol{\mathrm{lim}}\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\:}\frac{\mathrm{1}}{\mathrm{1}+\frac{\boldsymbol{\mathrm{r}}}{\boldsymbol{\mathrm{n}}}}\:=\:\underset{\mathrm{0}} {\overset{\mathrm{1}}…
Question Number 3017 by Filup last updated on 03/Dec/15 $${A}=\int_{\mu} ^{\:\mu+\epsilon} \:\frac{{dx}}{{x}+{n}} \\ $$$$ \\ $$$${A}=\mathrm{ln}\left({x}+{n}\right)\:\mid_{\mu} ^{\mu+\epsilon} \\ $$$$=\mathrm{ln}\left(\mu+\epsilon+{n}\right)−\mathrm{ln}\left(\mu+{n}\right) \\ $$$$=\mathrm{ln}\left(\frac{\mu+\epsilon+{n}}{\mu+{n}}\right) \\ $$$$=\mathrm{ln}\left(\frac{\mu+{n}}{\mu+{n}}+\frac{\epsilon}{\mu+{n}}\right) \\ $$$$…
Question Number 68549 by gunawan last updated on 13/Sep/19 $${y}=\frac{{x}^{\mathrm{3}} }{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$${y}^{−\mathrm{1}} =… \\ $$ Commented by mathmax by abdo last updated on…
Question Number 68546 by aliesam last updated on 13/Sep/19 $${find}\:{the}\:{range}\:{and}\:{domain}\:{of}\:{f}\left({x}\right) \\ $$$$ \\ $$$${f}\left({x}\right)=\sqrt{{sin}^{−\mathrm{1}} \left({ln}\frac{{x}}{\mathrm{10}}\right)} \\ $$ Answered by MJS last updated on 13/Sep/19 $$\sqrt{{u}}\in\mathbb{R}\:\Rightarrow\:{u}\geqslant\mathrm{0}…
Question Number 134079 by mnjuly1970 last updated on 27/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{mathematical}\:\:\:\:{analysis}….. \\ $$$$\:\:\:\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\:\:\:\mathrm{1}:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\Gamma\left({x}\right)\right){cos}^{\mathrm{2}} \left(\pi{x}\right){dx}=\frac{{ln}\left(\mathrm{2}\pi\right)}{\mathrm{4}}+\frac{\pi}{\mathrm{8}}\:..\checkmark \\ $$$$\:\:\:\:\:\:\mathrm{2}:\:\:{lim}_{{n}\rightarrow\infty} \frac{\Gamma\left({n}+\mathrm{1}\right)\Gamma\left({n}+\mathrm{2}\right)}{\Gamma^{\mathrm{2}} \left({n}+\frac{\mathrm{3}}{\mathrm{2}}\right)}\:=\mathrm{1}…\checkmark \\ $$ Answered by…
Question Number 68541 by Kunal12588 last updated on 13/Sep/19 Commented by Kunal12588 last updated on 13/Sep/19 $${please}\:{answer}\:{with}\:{explanation} \\ $$ Answered by mr W last updated…
Question Number 3003 by Rasheed Soomro last updated on 02/Dec/15 $${What}\:{is}\:{nth}\:{term}? \\ $$$$\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{5}}{\mathrm{4}},\frac{\mathrm{15}}{\mathrm{8}},\frac{\mathrm{37}}{\mathrm{16}},\frac{\mathrm{83}}{\mathrm{32}}… \\ $$ Commented by Rasheed Soomro last updated on 05/Dec/15 $$\underset{−} {\mathcal{HIGH}{ly}}\:\mathcal{A}{ppriciate}\:\mathcal{Y}{our}\:\overset{\mathcal{VALUEABLE}}…
Question Number 3001 by Filup last updated on 02/Dec/15 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{evaluate}: \\ $$$${S}=\underset{{i}={k}} {\overset{{n}} {\sum}}\:^{{n}} {C}_{{i}} \\ $$ Commented by Rasheed Soomro last updated on 02/Dec/15…
Question Number 134074 by EDWIN88 last updated on 27/Feb/21 Commented by EDWIN88 last updated on 27/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{r}\:=\:\mathrm{10}\:\mathrm{cm} \\ $$ Answered by bramlexs22 last updated on…
Question Number 68537 by naka3546 last updated on 13/Sep/19 Answered by MJS last updated on 13/Sep/19 $$\mathrm{1}\:\mathrm{8}\:\mathrm{17} \\ $$$$\mathrm{4}\:\mathrm{7}\:\mathrm{17} \\ $$$$\mathrm{4}\:\mathrm{13}\:\mathrm{13} \\ $$$$\mathrm{7}\:\mathrm{7}\:\mathrm{16} \\ $$$$\mathrm{8}\:\mathrm{11}\:\mathrm{13}…