Question Number 201715 by aurpeyz last updated on 11/Dec/23 $${Use}\:{Cauchy}\:{Riemann}\:{to}\:{verify}\:{whether}\: \\ $$$${f}\left({z}\right)=\frac{\mathrm{1}}{{z}\left({z}+\mathrm{1}\right)}\:{is}\:{analytic}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 201740 by MathedUp last updated on 12/Dec/23 $${y}''\left({t}\right)+\frac{\mathrm{g}}{\ell}\centerdot\mathrm{sin}\left({y}\left({t}\right)\right)=\mathrm{0} \\ $$$$\boldsymbol{\mathcal{L}}_{{s}} \left\{{y}''\left({t}\right)\right\}+\frac{\mathrm{g}}{\ell}\boldsymbol{\mathcal{L}}_{{s}} \left\{\mathrm{sin}\left({y}\left({t}\right)\right)\right\}=\mathrm{0} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} {y}''\left({t}\right){e}^{−{st}} \mathrm{d}{t}+\frac{\mathrm{g}}{\ell}\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{sin}\left({y}\left({t}\right)\right){e}^{−{st}} \mathrm{d}{t}=\mathrm{0} \\ $$$$\int_{\mathrm{0}} ^{\:\infty}…
Question Number 201764 by hardmath last updated on 11/Dec/23 $$\mathrm{1}.\:\mathrm{y}\:=\:\mathrm{tgx}\:−\:\mathrm{ctgx}\:\:\rightarrow\:\:\mathrm{y}^{'} \:=\:? \\ $$$$\mathrm{2}.\:\mathrm{y}\:=\:\left(\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} \right)\:\mathrm{arctgx}\:\rightarrow\:\mathrm{y}^{'} \:=\:? \\ $$$$\mathrm{3}.\:\mathrm{y}\:=\:\mathrm{cos}^{\mathrm{4}} \:\mathrm{x}\:\rightarrow\:\mathrm{y}^{'} \:=\:? \\ $$$$\mathrm{4}.\:\begin{cases}{\mathrm{x}\:=\:\mathrm{2t}}\\{\mathrm{y}\:=\:\mathrm{3t}^{\mathrm{2}} \:−\:\mathrm{5t}}\end{cases}\:\:\:\rightarrow\:\:\:\mathrm{x}^{'} \:,\:\mathrm{y}^{'} \:=\:? \\…
Question Number 201728 by hardmath last updated on 11/Dec/23 $$\mathrm{cos}^{\mathrm{2}} \:\mathrm{4x}\:\centerdot\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{4x}\:=\:\mathrm{0},\mathrm{25}\:\mathrm{for}\:\mathrm{equation} \\ $$$$\left[\mathrm{0};\mathrm{90}\right]\:\mathrm{how}\:\mathrm{many}\:\mathrm{roots}\:\mathrm{are}\:\mathrm{there}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{piece}? \\ $$ Answered by esmaeil last updated on 11/Dec/23…
Question Number 201729 by hardmath last updated on 11/Dec/23 The teacher can choose in 560 ways, provided that there are three students in each team.…
Question Number 201762 by Calculusboy last updated on 11/Dec/23 Answered by mr W last updated on 12/Dec/23 $$\int_{−\mathrm{2}} ^{\mathrm{2}} \left({x}^{\mathrm{3}} \mathrm{cos}\:\frac{{x}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\right)\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }\:{dx} \\ $$$$=\int_{−\mathrm{2}} ^{\mathrm{2}}…
Question Number 201763 by hardmath last updated on 11/Dec/23 $$\mathrm{Find}: \\ $$$$\mathrm{1}.\:\int\:\mathrm{cos3x}\:\mathrm{cosx}\:\mathrm{dx}\:=\:? \\ $$$$\mathrm{2}.\:\int\:\mathrm{3}^{\boldsymbol{\mathrm{x}}} \:\mathrm{sinx}\:\mathrm{dx}\:=\:? \\ $$$$\mathrm{3}.\:\int_{\mathrm{0}\:} ^{\:\mathrm{1}} \:\mathrm{x}\:\mathrm{e}^{−\boldsymbol{\mathrm{x}}} \:\mathrm{dx}\:=\:? \\ $$$$\mathrm{4}.\:\int_{\mathrm{1}} ^{\:\boldsymbol{\mathrm{e}}} \:\mathrm{ln}^{\mathrm{2}} \:\mathrm{x}\:\mathrm{dx}\:=\:?…
Question Number 201660 by LimPorly last updated on 10/Dec/23 $${An}\:{equilateral}\:{triangle}\:{inscribed}\:{in}\:{a}\:{parabola} \\ $$$${y}^{\mathrm{2}} =\mathrm{4}{x}.\:{One}\:{of}\:{its}\:{vertices}\:{is}\:{at}\:{the}\:{vertex}\:{of}\:\:{the}\:{parabola}. \\ $$$${Find}\:{the}\:{length}\:{of}\:{each}\:{side}\:{of}\:{the}\:{triangle}\:{in}\:{units}. \\ $$ Answered by som(math1967) last updated on 10/Dec/23 $$\:{slope}\:{of}\:{AB}\:={tan}\mathrm{30}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}…
Question Number 201657 by LimPorly last updated on 10/Dec/23 $${if}\:\:{f}\left({x}\right)=\begin{cases}{\frac{\mathrm{sin}\:\left(\mathrm{1}+\left[{x}\right]\right)}{\left[{x}\right]}\:\:{for}\:\left[{x}\right]\neq\mathrm{0}}\\{\mathrm{0}\:\:{for}\:\left[{x}\right]=\mathrm{0}}\end{cases} \\ $$$${where}\:\left[{x}\right]\:{represents}\:{an}\:{integer}\:\boldsymbol{{x}}\:{greatest}\:\leqslant\:\boldsymbol{{x}} \\ $$$${Find}\:\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}{f}\left({x}\right). \\ $$ Answered by aleks041103 last updated on 10/Dec/23…
Question Number 201659 by LimPorly last updated on 10/Dec/23 $${Find}\:{the}\:{shortest}\:{distance}\:{between}\: \\ $$$${point}\:{A}\left(\mathrm{3},\mathrm{2}\right)\:{and}\:{curve}\:{y}=\sqrt{{x}}\:\left({x}>\mathrm{0}\right). \\ $$ Answered by mr W last updated on 10/Dec/23 $${say}\:{the}\:{distance}\:{is}\:{s}. \\ $$$${say}\:{the}\:{point}\:{on}\:{the}\:{curve}\:{is}\:\left({p}^{\mathrm{2}}…