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Question Number 161014 Answers: 0 Comments: 0
Question Number 160953 Answers: 1 Comments: 0
$$\int_{{o}} ^{+{oo}} \:\frac{{tlnt}}{\left(\mathrm{1}+{t}\right)^{\mathrm{2}} }\:\:\:\: \\ $$$${etudier}\:{la}\:{convergence} \\ $$
Question Number 160950 Answers: 1 Comments: 0
Question Number 160949 Answers: 0 Comments: 0
Question Number 160948 Answers: 1 Comments: 0
$$\frac{\mathrm{1}}{\mathrm{1}\centerdot\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}\centerdot\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}\centerdot\mathrm{6}}+...+\frac{\mathrm{1}}{\mathrm{39}\centerdot\mathrm{40}}=? \\ $$
Question Number 160939 Answers: 2 Comments: 1
$${log}\underset{{ab}} {{x}}=?\:\:\:\:\:\:{if}\:\:{log}\underset{{a}} {{x}}=\mathrm{30}\:\:{andlog}\underset{{b}} {{x}}=\mathrm{70} \\ $$
Question Number 160938 Answers: 1 Comments: 0
$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\left(\frac{\pi}{\mathrm{cos}\:\mathrm{x}}\:−\mathrm{2x}\:\mathrm{tan}\:\mathrm{x}\:\right)=? \\ $$
Question Number 160937 Answers: 1 Comments: 0
$$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\:\mathrm{sin}\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}−\mathrm{sin}\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}\:\right)=? \\ $$
Question Number 160933 Answers: 1 Comments: 0
$$\:{In}\:{the}\:{given}\:{equation}\:{below}\:,\:{applying} \\ $$$${the}\:{formula}\:{for}\:{the}\:{derivative}\:{of} \\ $$$$\:{inverse}\:{trigonometric}\:{functions}\:, \\ $$$$\:{what}\:{is}\:{the}\:''{u}\:''\:{from}\:{the}\:{given}\:{function}. \\ $$$$\:{y}\:=\:\mathrm{cosec}^{−\mathrm{1}} \left[\:\mathrm{sin}\:\left(\frac{\mathrm{1}+\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}\right)\right] \\ $$
Question Number 160931 Answers: 1 Comments: 0
$$\:\:{x}\:=\:\mathrm{2}^{\mathrm{log}\:_{\mathrm{5}} \left({x}+\mathrm{3}\right)} \:;\:{x}=? \\ $$
Question Number 160928 Answers: 1 Comments: 0
$$ \\ $$$$\:\:\:\:\:\:\:{calculate} \\ $$$$ \\ $$$$\:\:\:\:\Omega\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\zeta\:\left(\:\mathrm{1}+\:{n}\:\right)\:−\mathrm{1}}{{n}\:+\:\mathrm{1}}\:\overset{?} {=}\:\mathrm{1}−\:\gamma\: \\ $$$$\:−−−−−−−−−−− \\ $$
Question Number 160924 Answers: 1 Comments: 1
Question Number 160923 Answers: 0 Comments: 1
$$\:\:\begin{cases}{\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2021}} =\:\mathrm{z}}\\{\left(\mathrm{x}+\mathrm{z}\right)^{\mathrm{2021}} \:=\:\mathrm{y}}\\{\left(\mathrm{y}+\mathrm{z}\right)^{\mathrm{2021}} \:=\:\mathrm{x}}\end{cases} \\ $$$$\:\:\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=... \\ $$
Question Number 160922 Answers: 1 Comments: 0
$${monter}\:{que}\:\left(\mathrm{3}+\sqrt{\mathrm{5}}\right)^{{n}} +\left(\mathrm{3}−\sqrt{\mathrm{5}}\right)^{{n}\:} \\ $$$${est}\:{divisible}\:{par}\:\mathrm{2}^{{n}} \\ $$$${beson}\:{d}'{aide}\:{svp} \\ $$
Question Number 160921 Answers: 0 Comments: 0
$$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{1}} {\overset{\:\mathrm{21}} {\int}}\:\frac{\mathrm{dx}}{\boldsymbol{\mathrm{e}}^{\left[\mathrm{2}\boldsymbol{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\right]} }\:\:\:;\:\:\:\left[\ast\right]-\mathrm{GIF} \\ $$
Question Number 160917 Answers: 1 Comments: 0
$${Calculate} \\ $$$$\left.{a}\right)\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\right)^{{x}^{\mathrm{2}} } \\ $$$$\left.{b}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2}^{\frac{\mathrm{1}}{{x}}} −\mathrm{1}}{\mathrm{2}^{\frac{\mathrm{1}}{{x}}} +\mathrm{1}} \\ $$
Question Number 160912 Answers: 1 Comments: 0
$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\mathrm{x}+\mathrm{2}\right)\mathrm{tan}\:\left(\mathrm{2}−\mathrm{x}\right)−\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{2}\right)}{\mathrm{3x}\:\mathrm{tan}\:\mathrm{x}}\:=? \\ $$
Question Number 160910 Answers: 1 Comments: 0
Question Number 160909 Answers: 2 Comments: 0
$${How}\:\:{many}\:\:\mathrm{3}−{digits}\:\:{number}\:\:{such}\:\:{that}\:\:{sum}\:\:{of}\:\:{its}\:\:{digits}\:\:{is}\:\:\mathrm{11}\:? \\ $$
Question Number 160908 Answers: 0 Comments: 1
$${x},{y},{z}\:\:\in\:\:\mathbb{R}^{+} \\ $$$${Find}\:\:{the}\:\:{minimum}\:\:{value}\:\:{of}\:\:{this}\:\:{expression}\: \\ $$$$\:\:\:\:\:\:\frac{{xyz}}{\left(\mathrm{1}+\mathrm{3}{x}\right)\left({x}+\mathrm{8}{y}\right)\left({y}+\mathrm{9}{z}\right)\left(\mathrm{6}+{z}\right)}\:\: \\ $$$$ \\ $$
Question Number 160906 Answers: 0 Comments: 0
Question Number 160903 Answers: 2 Comments: 0
$$\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}\:'=\:\mathrm{2}{xy}\:+\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} \: \\ $$
Question Number 160902 Answers: 1 Comments: 0
$$\:\:\int\:\frac{{dx}}{\:\sqrt{\mathrm{sin}\:^{\mathrm{3}} {x}}\:\sqrt{\mathrm{cos}\:^{\mathrm{5}} {x}}}\:=? \\ $$
Question Number 160900 Answers: 0 Comments: 2
$${Calculate} \\ $$$$\left.\mathrm{1}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{x}+\mathrm{1}}{\mathrm{2}{x}+\mathrm{1}}\right)^{{x}^{\mathrm{2}} } \\ $$$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:{a}}\right)^{\frac{\mathrm{1}}{{x}−{a}}} \\ $$
Question Number 160895 Answers: 1 Comments: 0
$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{x}^{\boldsymbol{\mathrm{n}}-\mathrm{1}} \:+\:...\:+\:\mathrm{1}}\:\mathrm{dx}\:=\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} }\:\left[\boldsymbol{\psi}^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{2}}{\mathrm{n}}\right)\:-\:\boldsymbol{\psi}^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{1}}{\mathrm{n}}\right)\right] \\ $$
Question Number 160894 Answers: 1 Comments: 0
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