Question Number 64444 by mathmax by abdo last updated on 18/Jul/19 $${calculate}\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{{k}}{\left({k}+\mathrm{1}\right)!} \\ $$ Commented by Prithwish sen last updated on 18/Jul/19…
Question Number 129978 by MJS_new last updated on 21/Jan/21 $$\mathrm{is}\:\mathrm{this}\:\mathrm{true}\:\mathrm{for}\:{n}\in\mathbb{N}^{\bigstar} ?\:\mathrm{someone}\:\mathrm{please}\:\mathrm{prove} \\ $$$$\mathrm{or}\:\mathrm{falsify}! \\ $$$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\mathrm{e}^{−{x}^{\mathrm{2}{n}} } {dx}=\Gamma\:\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{2}{n}} \\ $$ Answered by Dwaipayan Shikari…
Question Number 64443 by mathmax by abdo last updated on 18/Jul/19 $${find}\:{all}\:{functin}\:{f}\:{Z}\rightarrow{Z}\:\:{wich}\:{verify} \\ $$$$\forall\left({a},{b}\right)\in{Z}^{\mathrm{2}} \:\:\:\:\:{f}\left(\mathrm{2}{a}\right)+\mathrm{2}{f}\left({b}\right)\:={f}\left({f}\left({a}+{b}\right)\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 129979 by liberty last updated on 21/Jan/21 $$\mathrm{If}\:\begin{cases}{\mid\mathrm{x}\mid\:+\:\mathrm{x}\:+\:\mathrm{y}\:=\:\mathrm{5}}\\{\mathrm{x}\:+\:\mid\mathrm{y}\mid\:−\mathrm{y}\:=\:\mathrm{10}}\end{cases}\:\mathrm{then}\:\mathrm{x}+\mathrm{y}\:? \\ $$ Answered by MJS_new last updated on 21/Jan/21 $$\mid{x}\mid+{x}+{y}=\mathrm{5} \\ $$$${x}\leqslant\mathrm{0}\:\Rightarrow\:{y}=\mathrm{5} \\ $$$$\mathrm{but}\:\mathrm{then}\:\mathrm{the}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{eq}.\:\mathrm{gives}\:{x}=\mathrm{10}>\mathrm{0}…
Question Number 129975 by Algoritm last updated on 21/Jan/21 Answered by Olaf last updated on 21/Jan/21 $$\Omega\:=\:\int_{−\infty} ^{+\infty} {e}^{−\left(\frac{{x}}{{a}}\right)^{\mathrm{2}} } {dx} \\ $$$$\Omega\:=\:\mathrm{2}\mid{a}\mid\int_{\mathrm{0}} ^{+\infty} {e}^{−{u}^{\mathrm{2}}…
Question Number 129972 by mnjuly1970 last updated on 21/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{nice}\:\:{calculus}… \\ $$$$\:\:{evaluation}: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} {t}^{\mathrm{2}} {e}^{−{t}} {ln}\left({t}\right){dt}=?? \\ $$$$\:\:{solution}: \\ $$$$\:\:\:{f}\left({s}\right)=\int_{\mathrm{0}} ^{\:\infty}…
Question Number 129973 by mohammad17 last updated on 21/Jan/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 64436 by ajfour last updated on 17/Jul/19 Commented by ajfour last updated on 17/Jul/19 $${Find}\:{radius}\:{of}\:{arc}\:{length}\:{s}\:,\:{if} \\ $$$${area}\:{between}\:{parabola}\:{and}\:{arc} \\ $$$${is}\:{a}\:{maximum}. \\ $$ Answered by…
Question Number 64429 by mathmax by abdo last updated on 17/Jul/19 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{{t}+{x}+\sqrt{{t}^{\mathrm{2}} \:+\mathrm{1}}}\:\:\:\left({x}\:{real}\:{parametre}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicite}\:{form}\:{forf}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){detemine}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\left({t}+{x}+\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right){give}\:{f}^{\left({n}\right)}…
Question Number 64425 by Tawa1 last updated on 17/Jul/19 Commented by Prithwish sen last updated on 17/Jul/19 $$\mathrm{Area}\:\mathrm{of}\:\mathrm{shaded}\:\mathrm{portion}\:=\: \\ $$$$\mathrm{Area}\:\mathrm{of}\:\mathrm{square}\:−\:\mathrm{Area}\:\mathrm{of}\:\mathrm{quarter}\:\mathrm{circle} \\ $$$$=\:\mathrm{a}^{\mathrm{2}} \:−\:\frac{\pi\mathrm{a}^{\mathrm{2}} }{\mathrm{4}}\:\left[\:\mathrm{if}\:\boldsymbol{\mathrm{a}}\:\mathrm{be}\:\mathrm{the}\:\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}\right. \\…