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Question Number 184185 Answers: 1 Comments: 0
$$\mathrm{Differentiate},\:\mathrm{y}=\left(\mathrm{log}_{\mathrm{e}} \mathrm{x}\right)^{\mathrm{x}} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$
Question Number 184183 Answers: 0 Comments: 0
Question Number 184184 Answers: 1 Comments: 0
$$\mathrm{y}=\left(\mathrm{sinx}\right)^{\mathrm{x}} \\ $$$$ \\ $$$$\mathrm{Differentiate} \\ $$
Question Number 184175 Answers: 2 Comments: 0
Question Number 184160 Answers: 4 Comments: 1
$$\:\:{Given}\:\begin{cases}{{a}_{\mathrm{0}} =\mathrm{1}}\\{{a}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{3}{a}_{{n}} +\sqrt{\mathrm{5}{a}_{{n}} ^{\mathrm{2}} −\mathrm{4}}\:\right)}\end{cases} \\ $$$$\:\forall{n}\geqslant\mathrm{0}\:,\:{n}\in{I}\: \\ $$$$\:\:{find}\:{a}_{{n}} . \\ $$
Question Number 184159 Answers: 1 Comments: 1
$${prove}\:{that}\:\mathrm{0}^{\mathrm{0}} =\mathrm{1} \\ $$
Question Number 184144 Answers: 2 Comments: 0
$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\underset{\boldsymbol{\mathrm{m}}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\left(−\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}+\boldsymbol{\mathrm{m}}} }{\boldsymbol{\mathrm{nm}}\left(\boldsymbol{\mathrm{n}}+\boldsymbol{\mathrm{m}}\right)} \\ $$
Question Number 184136 Answers: 0 Comments: 0
$$\:\underset{\mathrm{0}} {\overset{\mathrm{2}{n}\pi} {\int}}\:{max}\left(\mathrm{sin}\:{x},\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\:{x}\right)\right)\:{dx}\:=?\: \\ $$$$\:\left[\:{n}\in\:{I}\:\right]\: \\ $$
Question Number 184135 Answers: 2 Comments: 1
Question Number 184126 Answers: 1 Comments: 0
Question Number 184125 Answers: 0 Comments: 0
Question Number 184121 Answers: 2 Comments: 4
Question Number 184112 Answers: 1 Comments: 1
$$\:\:\int\:\frac{{dx}}{\left({x}−\mathrm{1}\right)^{\mathrm{5}/\mathrm{6}} \left({x}+\mathrm{2}\right)^{\mathrm{7}/\mathrm{6}} }\:=? \\ $$
Question Number 184105 Answers: 2 Comments: 0
$$\:{We}\:{cut}\:{a}\:{square}\:{sheet}\:{of}\:{metal}\:{into}\:{equal}\:{thirteen} \\ $$$$\:{cross}\:{slices},\:{we}\:{measured}\:{its}\:{perimeter}\:{of}\:\mathrm{168}\:{cm} \\ $$$$\:{How}\:{much}\:{was}\:{the}\:{perimeter}\:{of}\:{the}\:{plate} \\ $$$$\:{before}\:{cutting}? \\ $$
Question Number 184103 Answers: 0 Comments: 0
$$\boldsymbol{\mathrm{evaluate}}\:\overset{\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\int}_{\mathrm{0}} \boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{x}}\right)} \boldsymbol{\mathrm{dx}} \\ $$
Question Number 184102 Answers: 1 Comments: 0
$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}^{\mathrm{4}} \left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)}{\:\sqrt{\mathrm{1}−\boldsymbol{\mathrm{x}}}}\boldsymbol{\mathrm{dx}} \\ $$
Question Number 184098 Answers: 1 Comments: 2
$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}^{\mathrm{2}} \left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)}{\mathrm{1}−\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}} \\ $$
Question Number 184095 Answers: 2 Comments: 0
Question Number 184093 Answers: 2 Comments: 0
Question Number 184091 Answers: 2 Comments: 1
Question Number 184085 Answers: 1 Comments: 0
$$\left(\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{xy}^{\mathrm{2}} \right)\mathrm{y}^{'} \:+\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{yx}^{\mathrm{2}} \:=\:\mathrm{0} \\ $$$$ \\ $$
Question Number 184084 Answers: 1 Comments: 0
Question Number 184083 Answers: 1 Comments: 0
$$ \\ $$$$\:\:\:\:{f}\left({x}\right)=\:{x}^{\:\mathrm{3}} \:+\mathrm{3}{x}^{\:\mathrm{2}} −{ax}\:\:\:{is}\:\: \\ $$$$\:\:\:\:\:{decreasing}\:{on}\:\:\left[\:−\mathrm{1}\:,\:\mathrm{2}\right] \\ $$$$\:\:\:\:\:\:{then}\:\:{which}\:\:{is}\:{correct}... \\ $$$$\:\:\:\:\:\mathrm{1}:\:\:\:\left[\:−\mathrm{3}\:,\mathrm{24}\right] \\ $$$$\:\:\:\:\:\mathrm{2}:\:\:\left[\:\mathrm{24}\:,\:+\infty\right) \\ $$$$\:\:\:\:\:\:\mathrm{3}:\:\left(−\infty\:,−\mathrm{3}\right] \\ $$$$\:\:\:\:\:\:\:\:\mathrm{4}\::\left(−\infty,\:−\mathrm{3}\right]\cup\left[\mathrm{24},\:+\infty\right) \\ $$$$ \\ $$
Question Number 184076 Answers: 0 Comments: 2
$$\mathrm{6647}^{\mathrm{3}} {mod}\mathrm{10000}=\mathrm{2023} \\ $$
Question Number 184066 Answers: 1 Comments: 0
$$\frac{{dy}}{{dx}}={y}\left({y}+\mathrm{2}\right).\:{find}\:\:{y}=? \\ $$
Question Number 184062 Answers: 1 Comments: 0
$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{\:\sqrt{{i}^{\mathrm{2}} +{i}}}\:>\:\mathrm{ln}\left({n}+\mathrm{1}\right) \\ $$
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