Question Number 2006 by Rasheed Soomro last updated on 29/Oct/15 $${Determine} \\ $$$$\left({i}\right)\:\:\frac{{d}}{{dx}}\left({x}^{{x}} \right)\:\:\:\:\:\:\:\:\:\:\:\left({ii}\right)\:\:\int{x}^{{x}} \:{dx} \\ $$ Answered by 123456 last updated on 29/Oct/15 $${y}={x}^{{x}}…
Question Number 67540 by mathmax by abdo last updated on 28/Aug/19 $${prove}\:{that}\:\:\:\mid\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}+{it}\right)\mid\:=\sqrt{\frac{\mathrm{2}\pi}{{e}^{\pi{t}} \:+{e}^{−\pi{t}} }} \\ $$$${and}\:\mid\Gamma\left(\mathrm{1}+{it}\right)\mid\:=\sqrt{\frac{\mathrm{2}\pi{t}}{{e}^{\pi{t}} −{e}^{−\pi{t}} }} \\ $$ Commented by ~ À ®…
Question Number 2005 by Rasheed Soomro last updated on 29/Oct/15 $${If}\:{f}\left({x}\right)\:{and}\:{g}\left({x}\right)\:{have}\:{no}\:{constant}\:{term}\:{then} \\ $$$${f}\:'\left({x}\right)={g}'\left({x}\right)\overset{?} {\:\Rightarrow\:}{f}\left({x}\right)={g}\left({x}\right)? \\ $$ Commented by prakash jain last updated on 30/Oct/15 $$\mathrm{If}\:{f}\left({x}\right)\neq{g}\left({x}\right)…
Question Number 2004 by Yozzi last updated on 29/Oct/15 $${Suppose}\:\mathrm{0}<{b}\leqslant{a}.\:{Show}\:{that}\:{the}\:{area}\:{of} \\ $$$${intersection}\:{E}\cap{F}\:{of}\:{the}\:{two}\:{regions} \\ $$$${defined}\:{by}\: \\ $$$${E}=\left\{\left({x},{y}\right):\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\leqslant\mathrm{1}\right\}\:{and} \\ $$$${F}=\left\{\left({x},{y}\right):\frac{{x}^{\mathrm{2}} }{{b}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{a}^{\mathrm{2}}…
Question Number 67538 by mathmax by abdo last updated on 28/Aug/19 $${prove}\:{that}\:\frac{\Gamma^{'} \left({z}\right)}{\Gamma\left({z}\right)}\:=−\gamma−\frac{\mathrm{1}}{{z}}\:−\sum_{{n}=\mathrm{1}} ^{\infty} \left(\frac{\mathrm{1}}{{z}+{n}}−\frac{\mathrm{1}}{{n}}\right) \\ $$ Commented by ~ À ® @ 237 ~…
Question Number 133072 by bemath last updated on 18/Feb/21 $$\mathrm{Show}\:\mathrm{that}\:\frac{\mathrm{5}}{\mathrm{2}−\sqrt[{\mathrm{4}}]{\mathrm{3}}}\:\mathrm{is}\:\mathrm{in}\:\mathrm{F}_{\mathrm{2}} \:\mathrm{by}\:\mathrm{expressing} \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{in}\:\mathrm{form}\:{a}_{\mathrm{1}} +{b}_{\mathrm{1}} \sqrt{{k}_{\mathrm{1}} }\:\mathrm{where} \\ $$$${a}_{\mathrm{1}} ,{b}_{\mathrm{1}} ,\:{k}_{\mathrm{1}} \:{are}\:{in}\:{F}_{\mathrm{1}} \\ $$ Answered by…
Question Number 67539 by mathmax by abdo last updated on 28/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{du}}{\mid{u}+{z}\mid^{\mathrm{2}} }\:\:{if}\:{z}\:={r}\:{e}^{{i}\theta} \:\:\:{and}\:−\pi<\theta<\pi \\ $$ Commented by ~ À ® @ 237…
Question Number 133075 by LUFFY last updated on 18/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} +{k}^{\mathrm{2}} }\right)\:{k}\in?????? \\ $$ Answered by Dwaipayan Shikari last updated on 18/Feb/21 $$\frac{\mathrm{1}}{\mathrm{2}{ik}}\underset{{n}=\mathrm{1}}…
Question Number 2001 by Fitrah last updated on 29/Oct/15 $${Prove}\:{that}\:: \\ $$$$\frac{\mathrm{1}}{\mathrm{15}}\:<\:\frac{\mathrm{1}}{\mathrm{2}}\:\centerdot\:\frac{\mathrm{3}}{\mathrm{4}}\:\centerdot\:\frac{\mathrm{5}}{\mathrm{6}}\:\centerdot\:\centerdot\:\centerdot\:\centerdot\:\centerdot\:\frac{\mathrm{99}}{\mathrm{100}}\:<\:\frac{\mathrm{1}}{\mathrm{10}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 67537 by mathmax by abdo last updated on 28/Aug/19 $${prove}\:{that}\:\frac{\mathrm{1}}{\Gamma\left({z}\right)}\:={z}\:{e}^{\gamma{z}} \:\prod_{{n}=\mathrm{1}} ^{\infty} \left(\mathrm{1}+\frac{{z}}{{n}}\right){e}^{−\frac{{z}}{{n}}} \\ $$ Commented by ~ À ® @ 237 ~…