Question Number 188806 by horsebrand11 last updated on 07/Mar/23 $${Find}\:{minimum}\:{value}\:{of}\: \\ $$$$\:\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{xy}+\mathrm{4}{y}+\mathrm{5}{y}^{\mathrm{2}} −{x}\: \\ $$$$\:{for}\:{x}\:{and}\:{y}\:{real}\:{numbers} \\ $$ Answered by mr W last updated on…
Question Number 123243 by benjo_mathlover last updated on 24/Nov/20 $$\:{What}\:{is}\:{the}\:{shortest}\:{distance} \\ $$$${between}\:{two}\:{parabolas}\: \\ $$$${y}^{\mathrm{2}} \:=\:{x}−\mathrm{2}\:{and}\:{x}^{\mathrm{2}} \:=\:{y}−\mathrm{2}\:. \\ $$ Commented by liberty last updated on 24/Nov/20…
Question Number 123124 by aupo14 last updated on 23/Nov/20 Commented by Dwaipayan Shikari last updated on 23/Nov/20 $${x}!=\Gamma\left({x}+\mathrm{1}\right) \\ $$$${log}\left({x}!\right)={log}\left(\Gamma\left({x}+\mathrm{1}\right)\right) \\ $$$$\frac{\frac{{dx}!}{{dx}}}{{x}!}=\frac{\Gamma'\left({x}+\mathrm{1}\right)}{\Gamma\left({x}+\mathrm{1}\right)} \\ $$$$\Rightarrow\frac{{d}}{{dx}}\left({x}!\right)={x}!.\psi\left({x}+\mathrm{1}\right) \\…
Question Number 123051 by simplyjerico last updated on 22/Nov/20 $${e}^{{y}} =\mathrm{ln}\left(\mathrm{x}^{\mathrm{3}} +\mathrm{3y}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 188534 by thotasandeep111 last updated on 03/Mar/23 Answered by mr W last updated on 03/Mar/23 $$\int{f}\left({x}\right){dx}={f}\left({x}\right) \\ $$$$\Rightarrow{f}\left({x}\right)={e}^{{x}} \\ $$$$\int\left({f}\left({x}\right)\right)^{\mathrm{2}} {dx}=\int{e}^{\mathrm{2}{x}} {dx}=\frac{{e}^{\mathrm{2}{x}} }{\mathrm{2}}+{C}=\frac{\left({f}\left({x}\right)\right)^{\mathrm{2}}…
Question Number 57415 by Abdo msup. last updated on 03/Apr/19 $${solve}\:\left({x}−\mathrm{1}\right){y}^{'} \:+\left(\mathrm{1}+\sqrt{{x}}\right){y}\:={x}\:{e}^{−\mathrm{2}{x}} \\ $$ Commented by maxmathsup by imad last updated on 12/Apr/19 $${due}\:{to}\:\sqrt{{x}}{we}\:{must}\:{have}\:{x}\geqslant\mathrm{0}\:\:\:\left({ed}\right)\:\Leftrightarrow\left(\sqrt{{x}}−\mathrm{1}\right)\left(\sqrt{{x}}+\mathrm{1}\right){y}^{'} +\left(\sqrt{\:{x}}+\mathrm{1}\right){y}\:={xe}^{−\mathrm{2}{x}}…
Question Number 122945 by CanovasCamiseros last updated on 21/Nov/20 Commented by CanovasCamiseros last updated on 21/Nov/20 $$\boldsymbol{{Question}}\:\left(\boldsymbol{{b}}\right) \\ $$ Answered by TANMAY PANACEA last updated…
Question Number 188387 by cortano12 last updated on 28/Feb/23 Answered by Frix last updated on 28/Feb/23 $$\mathrm{I}\:\mathrm{think}\:\mathrm{because}\:\mathrm{of}\:\mathrm{symmetry}\:{a}={b}={c}=\mathrm{1}\:\Rightarrow \\ $$$$\mathrm{Minimum}\:\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Answered by mnjuly1970 last…
Question Number 122704 by mnjuly1970 last updated on 19/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:…\:{general}\:\:{calculus}… \\ $$$$\:{i}:\:\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\mathrm{4}{x}}}\:\overset{??} {=}\underset{{n}=\mathrm{0}\:} {\overset{\infty} {\sum}}\left[\begin{pmatrix}{\mathrm{2}{n}}\\{\:{n}}\end{pmatrix}\:\:{x}^{{n}} \right] \\ $$$$\:{ii}:\:\frac{\pi}{\mathrm{2}}\:\overset{?} {=}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left[\frac{\begin{pmatrix}{\mathrm{2}{n}}\\{\:{n}}\end{pmatrix}}{\mathrm{4}^{{n}} }\:\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)}\right] \\ $$$$\:\:\:\:\:\:\:\:\:\: \\…
Question Number 122695 by liberty last updated on 19/Nov/20 $${Find}\:{maximum}\:{and}\:{minimum}\:{values} \\ $$$${of}\:{f}\left({x},{y}\right)\:=\:{xy}\:{on}\:{the}\:{circle}\:{g}\left({x},{y}\right)= \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{1}=\mathrm{0}\:. \\ $$ Answered by john santu last updated on…