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 $$\mathrm{x}^{\mathrm{3}} −\mathrm{6x}^{\mathrm{2}} +\mathrm{12x}−\mathrm{32}=\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{3}} −\mathrm{24} \\ $$$$\mathrm{x}−\mathrm{2}=\mathrm{y} \\ $$$$\Leftrightarrow\sqrt[{\mathrm{3}}]{\mathrm{y}+\mathrm{24}}=\mathrm{y}^{\mathrm{3}} −\mathrm{24}…
Question Number 201679 by cherokeesay last updated on 10/Dec/23 Answered by Rasheed.Sindhi last updated on 10/Dec/23 $$\sqrt[{\mathrm{6}}]{\mathrm{1}−\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:+\sqrt[{\mathrm{6}}]{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:−\mathrm{1}}\:=\mathrm{1} \\ $$$${a}+{b}=\mathrm{1}\Rightarrow{b}=\mathrm{1}−{a} \\ $$$${a}^{\mathrm{6}} +{b}^{\mathrm{6}} =\mathrm{1}−\sqrt{{x}^{\mathrm{2}}…
Question Number 201629 by ali009 last updated on 09/Dec/23 Commented by ali009 last updated on 09/Dec/23 $${how}\:{is}\:{that}\:{cslculated}? \\ $$ Commented by aleks041103 last updated on…
Question Number 201613 by hardmath last updated on 09/Dec/23 $$\mathrm{x},\mathrm{y},\mathrm{z}\:\in\:\mathbb{R} \\ $$$$\begin{cases}{\mathrm{xy}\:+\:\mathrm{yz}\:+\:\mathrm{zx}\:=\:\mathrm{3}}\\{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{5}}\end{cases}\:\:\:\:\:\rightarrow\:\:\:\:\mathrm{max}\left(\boldsymbol{\mathrm{z}}\right)\:=\:? \\ $$ Answered by aleks041103 last updated on 09/Dec/23 $${x}+{y}+{z}=\mathrm{5}\Rightarrow{z}=\mathrm{5}−{x}−{y} \\ $$$$\Rightarrow{xy}+\left({x}+{y}\right)\left(\mathrm{5}−\left({x}+{y}\right)\right)=\mathrm{3} \\…
Question Number 201615 by hardmath last updated on 09/Dec/23 $$\mathrm{x},\mathrm{y},\mathrm{z}\:\in\:\mathbb{R} \\ $$$$\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0} \\ $$$$\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}}\:+\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{b}}\:+\:\frac{\mathrm{z}^{\mathrm{2}} }{\mathrm{c}}\:\geqslant\:\frac{\left(\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\right)^{\mathrm{2}} }{\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}} \\ $$ Answered by AST…