Question Number 120553 by snipers237 last updated on 01/Nov/20 $$\:\: \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\infty} \mid\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\:−{ix}\right)\mid^{\mathrm{2}} {dx}\:=\:\frac{\pi}{\mathrm{2}}\: \\ $$ Answered by mnjuly1970 last updated on 01/Nov/20 $${solution}:\:…
Question Number 120528 by snipers237 last updated on 01/Nov/20 $${Let}\:\:{a}>\mathrm{0}\:,\:{g}\left({x}\right)=\underset{{n}\in\mathbb{Z}} {\sum}{exp}\left(−\frac{\left({x}−{n}\right)^{\mathrm{2}} }{{a}}\right) \\ $$$${Find}\:{the}\:{Fourier}\:{coefficients}\:{of}\:\:\:{g} \\ $$$${and}\:{deduce}\:{that}\:{for}\:{x}\in\mathbb{R}^{\ast} \\ $$$$\:\underset{{n}\in\mathbb{Z}} {\sum}{exp}\left(−\frac{\pi{n}^{\mathrm{2}} }{{x}^{\mathrm{2}} }\right)=\:{x}\:.\underset{{n}\in\mathbb{Z}} {\sum}{exp}\left(−\pi{n}^{\mathrm{2}} {x}^{\mathrm{2}} \right) \\…
Question Number 186027 by Michaelfaraday last updated on 31/Jan/23 Answered by qaz last updated on 31/Jan/23 $$\frac{{d}\mid{y}\mid}{{dx}}=\begin{vmatrix}{\mathrm{sin}\:{x}}&{\mathrm{sin}\:{x}}\\{−\mathrm{sin}\:{x}}&{−\mathrm{sin}\:{x}}\end{vmatrix}+\begin{vmatrix}{\mathrm{cos}\:{x}}&{\mathrm{cos}\:{x}}\\{\mathrm{cos}\:{x}}&{\mathrm{cos}\:{x}}\end{vmatrix}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 120463 by bramlexs22 last updated on 31/Oct/20 $${Find}\:{the}\:{slope}\:{of}\:{the}\:{line}\:{tangent} \\ $$$${to}\:{the}\:{graph}\:{r}=\mathrm{3cos}\:^{\mathrm{2}} \left(\mathrm{2}\theta\right)\:{at} \\ $$$$\theta=\frac{\pi}{\mathrm{6}}.\: \\ $$ Answered by mr W last updated on 31/Oct/20…
Question Number 120452 by john santu last updated on 31/Oct/20 $${Find}\:{the}\:{equation}\:{of}\:{the}\:{line}\:{tangent}\:{to}\:{the}\:{parametric} \\ $$$${curve}\:{given}\:{by}\:{the}\:{equations}\:\begin{cases}{{x}=\left(\mathrm{1}+{t}^{\mathrm{3}} \right)^{\mathrm{4}} +{t}^{\mathrm{2}} }\\{{y}={t}^{\mathrm{5}} +{t}^{\mathrm{2}} +\mathrm{2}}\end{cases}\:{at}\:{t}=\mathrm{1} \\ $$ Answered by physicstutes last updated…
Question Number 120378 by john santu last updated on 31/Oct/20 $${find}\:{the}\:{point}\:{on}\:{the}\:{curve}\:\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}{y}^{\mathrm{2}} =\mathrm{72} \\ $$$${closest}\:{to}\:{line}\:\mathrm{3}{x}+\mathrm{2}{y}−\mathrm{1}=\mathrm{0} \\ $$ Commented by bramlexs22 last updated on 31/Oct/20 $${let}\:\left({x},{y}\right)\:{is}\:{a}\:{point}\:{on}\:{hyperbola}…
Question Number 120322 by sdfg last updated on 30/Oct/20 Commented by TANMAY PANACEA last updated on 30/Oct/20 $${do}\:{x}'\:{means}\:=\frac{{dx}}{{dt}}\:{pls}… \\ $$ Commented by Dwaipayan Shikari last…
Question Number 120312 by mnjuly1970 last updated on 30/Oct/20 $$\:\:\:\:\:\:\:\:\:\:…\:\clubsuit{nice}\:\:{calculus}\clubsuit… \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:{lim}_{{n}\rightarrow\infty} \frac{\sqrt[{{n}^{\mathrm{2}} }]{{n\$}}}{\:\sqrt{{n}}}?\overset{???} {=}{e}^{\frac{−\mathrm{3}}{\mathrm{4}}} \\ $$$$\:\:\:\:\:{where}\:::\:\:{n\$}\:\overset{{superfactorial}} {=}{n}!.\left({n}−\mathrm{1}\right)!.\left({n}−\mathrm{2}\right)!…\mathrm{3}!.\mathrm{2}!.\mathrm{1}! \\ $$$$\:\:\:\:\:\:\:\:…\spadesuit{m}.{n}.\mathrm{1970}\spadesuit… \\…
Question Number 120243 by benjo_mathlover last updated on 30/Oct/20 Answered by bemath last updated on 30/Oct/20 $${let}\:{f}\left({x}\right)\:=\:{x}^{\frac{\mathrm{1}}{{x}^{\mathrm{6}} }} \:\Leftrightarrow\:\mathrm{ln}\:{f}\left({x}\right)=\:\frac{\mathrm{ln}\:\left({x}\right)}{{x}^{\mathrm{6}} } \\ $$$${differentiating}\:{both}\:{sides}\:{gives} \\ $$$$\frac{{f}\:'\left({x}\right)}{{f}\left({x}\right)}\:=\:\frac{{x}^{\mathrm{5}} −\mathrm{6}{x}^{\mathrm{5}}…
Question Number 120233 by MehraGanesh last updated on 30/Oct/20 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com