Question Number 8490 by fernandodantas1996 last updated on 14/Oct/16 $${show}\:{thats}\:{true}: \\ $$$$\int_{−\infty} ^{+\infty} {e}^{−{x}^{\mathrm{2}} } =\:\sqrt{\pi} \\ $$ Commented by prakash jain last updated on…
Question Number 74024 by ajfour last updated on 18/Nov/19 $$\begin{cases}{{h}^{\mathrm{2}} +{y}^{\mathrm{2}} +\left({k}−{z}\right)^{\mathrm{2}} ={s}^{\mathrm{2}} }\\{{a}^{\mathrm{2}} +\left({b}−{y}\right)^{\mathrm{2}} +{z}^{\mathrm{2}} ={s}^{\mathrm{2}} }\\{{ah}+{y}\left({y}−{b}\right)+{z}\left({z}−{k}\right)=\mathrm{0}}\\{\frac{{h}+{a}}{\mathrm{2}}+{yz}−\left({b}−{y}\right)\left({k}−{z}\right)=\mathrm{1}}\\{{b}+{a}\left({k}−{z}\right)+{hz}=\mathrm{1}}\\{{k}+{h}\left({b}−{y}\right)+{ay}=\mathrm{1}}\end{cases} \\ $$$${Find}\:\:{s}_{{min}} \:{or}\:{at}\:{least}\:{express} \\ $$$$\:{s}={f}\left({y}\right)\:{or}\:{g}\left({z}\right). \\ $$…
Question Number 8488 by Basant007 last updated on 12/Oct/16 $${find}\:{y}_{{n}} \:{if}\:{y}=\mathrm{cos}\:\mathrm{2}{x} \\ $$ Commented by FilupSmith last updated on 13/Oct/16 $${y}_{{n}} =\frac{{d}^{{n}} {y}}{{dx}^{{n}} } \\…
Question Number 139556 by mnjuly1970 last updated on 28/Apr/21 $$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:……..\:{advanced}\:…\:…\:…\:{calculus}…….. \\ $$$$\:\:\:\Phi=\:{lim}_{{n}\rightarrow\infty} \left\{\int_{\mathrm{1}} ^{\:{n}} \frac{{x}}{\left[{x}\right]^{\mathrm{2}} }\:{dx}\:−\psi\left({n}+\mathrm{1}\right)\right\}=? \\ $$$$\:\:\:\:{solution}: \\ $$$$\:\:\:\:\:\Phi_{{n}} =\int_{\mathrm{1}} ^{\:{n}} \frac{{x}}{\left[{x}\right]^{\mathrm{2}}…
Question Number 8486 by PradipGos. last updated on 12/Oct/16 $$\underset{−\infty} {\overset{\infty} {\int}}{e}^{−\mathrm{2}\mid{x}\overset{} {\mid}\:} \left(\mathrm{1}−\mathrm{cos}\:\mathrm{2}\alpha{x}\right){dx}=???? \\ $$$${solve}\:{this}\:……. \\ $$$$ \\ $$$$ \\ $$ Answered by Yozzias…
Question Number 74019 by mathmax by abdo last updated on 17/Nov/19 $${let}\:{the}\:{matrix}\:\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:−\mathrm{3}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{{n}} \:\:{for}\:{n}\:{integr} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{e}^{{A}} \:\:{and}\:{e}^{−{A}} . \\ $$ Commented by mathmax by…
Question Number 139555 by snipers237 last updated on 28/Apr/21 $$\:\:\underset{{i}=\mathrm{0}} {\overset{\mathrm{5}} {\prod}}\left(\mathrm{1}−{cotan}\left(\mathrm{20}+{i}\right)\right)\:\:\overset{?} {=}\:\mathrm{8} \\ $$ Answered by mr W last updated on 28/Apr/21 $$\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{tan}\:\mathrm{20}°}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{tan}\:\mathrm{25}°}\right) \\…
Question Number 74016 by mathmax by abdo last updated on 17/Nov/19 $${let}\:{g}\left({x}\right)\:=\frac{\mathrm{1}}{{x}}\int_{{x}} ^{\mathrm{2}{x}+\mathrm{1}} \:\:{arctan}\left({xt}\right){dt} \\ $$$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:{g}\left({x}\right)\:\:{and}\:{lim}_{{x}\rightarrow+\infty} {g}\left({x}\right). \\ $$ Commented by mathmax by abdo…
Question Number 74017 by mathmax by abdo last updated on 17/Nov/19 $${let}\:{f}\left({x}\right)=\int_{{x}} ^{{x}^{\mathrm{2}} +\mathrm{3}} \:{e}^{−{xt}} \:{ln}\left(\mathrm{1}+{e}^{−{xt}} \right){dt}\:\:\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right). \\ $$ Commented…
Question Number 74014 by mathmax by abdo last updated on 17/Nov/19 $$\:\: \\ $$$$\:\:{let}\:{W}\left({x}\right)=\sum_{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} \:\:\frac{{x}^{{i}+{j}} }{{ij}} \\ $$$${calculate}\:{W}\:^{'} \left({x}\right). \\ $$ Commented by mathmax by…