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Question Number 156107 Answers: 1 Comments: 1
$$\:\:\:\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}+\mathrm{1}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2019}}\right)^{\mathrm{2019}} \\ $$
Question Number 156106 Answers: 0 Comments: 0
$$\mathrm{Find}\:\mathrm{an}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tangen}\:\mathrm{line} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:\mathrm{the}\:\mathrm{given}\:\mathrm{equation}\: \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{indicated}\:\mathrm{point}\:\mathrm{P} \\ $$$$\left.\mathrm{1}\right).\:\:\mathrm{xy}+\mathrm{16}=\mathrm{0}\:\rightarrow\mathrm{P}\left(−\mathrm{2},\mathrm{8}\right) \\ $$$$\left.\mathrm{2}\right).\:\:\mathrm{y}^{\mathrm{2}} −\mathrm{4x}^{\mathrm{2}} =\mathrm{5}\rightarrow\mathrm{P}\left(−\mathrm{1},\mathrm{3}\right) \\ $$$$\left.\mathrm{3}\right).\:\:\mathrm{2x}^{\mathrm{3}} −\mathrm{x}^{\mathrm{2}} \mathrm{y}+\mathrm{y}^{\mathrm{3}} −\mathrm{1}=\mathrm{0}\rightarrow\mathrm{P}\left(\mathrm{2},−\mathrm{3}\right) \\ $$$$\left.\mathrm{4}\right).\:\:\mathrm{3y}^{\mathrm{4}} +\mathrm{4x}−\mathrm{x}^{\mathrm{2}} \mathrm{sin}\:\mathrm{y}−\mathrm{4}=\mathrm{0}\rightarrow\mathrm{P}\left(\mathrm{1},\mathrm{0}\right) \\ $$$$\left.\mathrm{5}\right).\:\:\mathrm{y}^{\mathrm{4}} +\mathrm{3}\:\mathrm{y}−\mathrm{4x}^{\mathrm{2}} =\mathrm{5x}+\mathrm{1}\rightarrow\mathrm{P}\left(\mathrm{1},−\mathrm{2}\right) \\ $$
Question Number 156103 Answers: 0 Comments: 0
Question Number 156102 Answers: 0 Comments: 0
Question Number 156086 Answers: 0 Comments: 4
$$\psi^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{1}}{\mathrm{6}}\right)\:-\:\psi^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{5}}{\mathrm{6}}\right)\:=\:\mathrm{10}\psi^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{1}}{\mathrm{3}}\right)\:-\:\frac{\mathrm{20}}{\mathrm{3}}\pi^{\mathrm{2}} \\ $$$$ \\ $$
Question Number 156085 Answers: 0 Comments: 0
$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\left(\mathrm{sin2x}\:+\:\mathrm{4cos}^{\mathrm{2}} \mathrm{x}\:+\:\mathrm{1}\right)\left(\mathrm{cos5x}\:-\:\mathrm{cosx}\right)<\mathrm{0} \\ $$$$ \\ $$
Question Number 156082 Answers: 0 Comments: 0
$$ \\ $$$$\:\:\:\:\:\mathrm{0}<\:\alpha\:<\frac{\pi}{\mathrm{2}}\:\:\: \\ $$$$\left.\:\:\sqrt[{\:\mathrm{3}}]{\:{sin}\left(\alpha\right)}\:+\:\sqrt[{\mathrm{3}}]{{cos}\left(\alpha\right.}\right)=\:\sqrt[{\mathrm{3}}]{\:{tan}\left(\alpha\right)} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\frac{\:{tan}\:\left(\alpha\:\right)\:+\:{cot}\:\left(\alpha\:\right)}{\mathrm{2}}\:=? \\ $$
Question Number 156080 Answers: 0 Comments: 1
$$\int{e}^{−\mathrm{2}{x}} {cos}\left({e}^{−{x}} \right){dx} \\ $$
Question Number 156072 Answers: 0 Comments: 5
Question Number 156065 Answers: 0 Comments: 0
$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{expression}\:\mathrm{M}=\boldsymbol{\mathrm{cos}}\frac{\boldsymbol{\mathrm{A}}−\boldsymbol{\mathrm{B}}}{\mathrm{2}}\mathrm{sin}\frac{\boldsymbol{\mathrm{A}}}{\mathrm{2}}\mathrm{sin}\frac{\boldsymbol{\mathrm{B}}}{\mathrm{2}} \\ $$
Question Number 156063 Answers: 3 Comments: 2
$$\:\:\:\:\frac{\mathrm{2}}{\mathrm{x}}+\frac{\mathrm{3}}{\mathrm{x}+\mathrm{1}}+\frac{\mathrm{4}}{\mathrm{x}+\mathrm{2}}+\frac{\mathrm{5}}{\mathrm{x}+\mathrm{3}}+\frac{\mathrm{6}}{\mathrm{x}+\mathrm{4}}=\mathrm{5} \\ $$
Question Number 156077 Answers: 1 Comments: 0
Question Number 156061 Answers: 2 Comments: 0
Question Number 156059 Answers: 1 Comments: 1
Question Number 156058 Answers: 1 Comments: 0
$$\:\:{cos}\frac{\pi}{\mathrm{8}}=...?\:\:{with}\:{solution}\:{plz} \\ $$
Question Number 156052 Answers: 0 Comments: 0
Question Number 156049 Answers: 0 Comments: 0
Question Number 156047 Answers: 0 Comments: 4
Question Number 156028 Answers: 1 Comments: 0
$$ \\ $$$$\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \sqrt{{sin}\left({x}\right)}\:\mathrm{ln}\left({sin}\left(\:{x}\:\right)\right){dx}=? \\ $$$$\:\:{m}.{n}.. \\ $$$$ \\ $$
Question Number 156024 Answers: 1 Comments: 0
Question Number 156021 Answers: 0 Comments: 0
Question Number 156009 Answers: 0 Comments: 5
$$\mathrm{Please}\:\mathrm{calculate} \\ $$$$\left.\mathrm{1}\right).\:\int\mathrm{sin}\:^{\mathrm{5}} \mathrm{x}\:\mathrm{dx} \\ $$$$\left.\mathrm{2}\right).\:\int\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx} \\ $$$$\left.\mathrm{3}\right).\:\int\mathrm{tan}\:^{\mathrm{3}} \mathrm{x}.\mathrm{sec}\:^{\mathrm{5}} \mathrm{x}\:\mathrm{dx} \\ $$$$\left.\mathrm{4}\right).\:\int\mathrm{cos}\:\mathrm{5x}.\mathrm{cos}\:\mathrm{3x}\:\mathrm{dx} \\ $$$$\left.\mathrm{5}\right).\:\int\:\:\frac{\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}−\mathrm{1}}{\mathrm{sec}\:^{\mathrm{2}} \:\mathrm{x}}\:\:\mathrm{dx} \\ $$
Question Number 156008 Answers: 0 Comments: 8
$$\mathrm{Tekhnic}\:\:\mathrm{Integration}\:\mathrm{by}\:\mathrm{part} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Find}\:\int\mathrm{x}.\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{Find}\:\int\mathrm{x}.\mathrm{e}^{\mathrm{2x}} \:\mathrm{dx} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{Find}\:\int\mathrm{ln}\:\:\mathrm{x}\:\mathrm{dx} \\ $$$$\left.\mathrm{4}\right)\:\:\mathrm{Find}\:\int\mathrm{x}^{\mathrm{2}} .\mathrm{e}^{\mathrm{2x}} \:\mathrm{dx} \\ $$$$\left.\mathrm{5}\right)\:\:\mathrm{Find}\:\int\mathrm{e}^{\mathrm{x}} \:\mathrm{cos}\:\mathrm{x}\:\mathrm{dx} \\ $$$$\: \\ $$$$ \\ $$
Question Number 156005 Answers: 2 Comments: 2
$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{{x}}{{sin}\left({x}\right)}\:{dx} \\ $$
Question Number 156055 Answers: 1 Comments: 0
Question Number 155996 Answers: 1 Comments: 0
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