Question Number 201796 by ajfour last updated on 12/Dec/23 $${x}^{\mathrm{4}} −\mathrm{15}{x}^{\mathrm{2}} −\mathrm{30}{x}+\mathrm{104}=\mathrm{0} \\ $$$${for}\:{x}\in\mathbb{R}\:\:\:\:\:{x}=\mathrm{2},\:\mathrm{4} \\ $$$${I}\:{want}\:{to}\:{know}\:{the}\:{best}\:{way}\:{to} \\ $$$${arrive}\:{at}\:{these}\:{answers}\:\left({without}\right. \\ $$$$\left.{guessing}\right).\:{I}\:{found}\:{one}\:{new}\:{way}. \\ $$$$\:{Shall}\:{post}\:{later}. \\ $$ Commented…
Question Number 201798 by hardmath last updated on 12/Dec/23 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}: \\ $$$$\boldsymbol{\mathrm{y}}\:=\:\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:−\:\mathrm{1}} \\ $$ Answered by dimentri last updated on 12/Dec/23 $$\:{y}=\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}\:\Rightarrow{y}'=\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}=\frac{{x}}{{y}}…
Question Number 201722 by Calculusboy last updated on 11/Dec/23 Commented by Frix last updated on 11/Dec/23 $$\mathrm{There}\:\mathrm{also}\:\mathrm{should}\:\mathrm{be}\:\mathrm{complex}\:\mathrm{solutions} \\ $$ Answered by Sutrisno last updated on…
Question Number 201715 by aurpeyz last updated on 11/Dec/23 $${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 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 201763 by hardmath last updated on 11/Dec/23 $$\mathrm{Find}: \\ $$$$\mathrm{1}.\:\int\:\mathrm{cos3x}\:\mathrm{cosx}\:\mathrm{dx}\:=\:? \\ $$$$\mathrm{2}.\:\int\:\mathrm{3}^{\boldsymbol{\mathrm{x}}} \:\mathrm{sinx}\:\mathrm{dx}\:=\:? \\ $$$$\mathrm{3}.\:\int_{\mathrm{0}\:} ^{\:\mathrm{1}} \:\mathrm{x}\:\mathrm{e}^{−\boldsymbol{\mathrm{x}}} \:\mathrm{dx}\:=\:? \\ $$$$\mathrm{4}.\:\int_{\mathrm{1}} ^{\:\boldsymbol{\mathrm{e}}} \:\mathrm{ln}^{\mathrm{2}} \:\mathrm{x}\:\mathrm{dx}\:=\:?…
Question Number 201702 by hardmath last updated on 10/Dec/23 $$\mathrm{Find}: \\ $$$$\int_{\mathrm{1}} ^{\:\mathrm{3}} \:\mathrm{dx}\:\int_{\boldsymbol{\mathrm{x}}} ^{\:\boldsymbol{\mathrm{x}}^{\mathrm{3}} } \:\left(\mathrm{x}\:−\:\mathrm{y}\right)\:\mathrm{dy} \\ $$ Commented by mr W last updated…
Question Number 201689 by cherokeesay last updated on 10/Dec/23 Answered by witcher3 last updated on 10/Dec/23 $$\mathrm{x}^{\mathrm{3}} −\mathrm{6x}^{\mathrm{2}} +\mathrm{12x}−\mathrm{32}=\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{3}} −\mathrm{24} \\ $$$$\mathrm{x}−\mathrm{2}=\mathrm{y} \\ $$$$\Leftrightarrow\sqrt[{\mathrm{3}}]{\mathrm{y}+\mathrm{24}}=\mathrm{y}^{\mathrm{3}} −\mathrm{24}…