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Question Number 149349 Answers: 0 Comments: 0
Question Number 149339 Answers: 1 Comments: 0
$$\:\:\:\:\:\:\:\:\:\:...{nice}......{mathematics}... \\ $$$$\:\:\:\:\:\:{ln}\left(\:\mathrm{2}\right)\:−\underset{{n}=\mathrm{1}\:} {\overset{\infty} {\sum}}\frac{\zeta\:\left(\:\mathrm{2}{n}+\mathrm{1}\:\right)−\mathrm{1}}{{n}\:+\:\mathrm{1}}\:=\:? \\ $$$$\:\:\:\:....{m}.{n}.... \\ $$
Question Number 149331 Answers: 1 Comments: 2
Question Number 149329 Answers: 1 Comments: 1
Question Number 149323 Answers: 2 Comments: 0
$${How}\:\:{many}\:\:{ordered}\:\:{pairs}\:\left({a},{b}\right)\:{with}\:\:{b}\:<\:{a}\:<\:\mathrm{100}\:\:,\:\:{a},{b}\:\in\:\mathbb{N}\:\:{such}\:\:{that}\:\:\frac{{a}}{{b}}\:\:{both}\:\:\:\frac{{a}+\mathrm{1}}{{b}+\mathrm{1}}\:\:{are}\:\:{integers}\:\:.\: \\ $$
Question Number 149322 Answers: 0 Comments: 5
$$\frac{\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\left(\sqrt{\mathrm{10}\:+\:\sqrt{\boldsymbol{{n}}}}\right)}{\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\left(\sqrt{\mathrm{10}\:-\:\sqrt{\boldsymbol{{n}}}}\right)}\:=\:? \\ $$
Question Number 149317 Answers: 2 Comments: 0
$${lim}_{{x}\rightarrow\infty} \sqrt{{x}^{\mathrm{6}} +\mathrm{5}{x}^{\mathrm{3}} }−{x} \\ $$
Question Number 149309 Answers: 3 Comments: 0
$${if}\:\:\:\:{t}={tanx}\:{what}\:{is}\:{the}\:{value}\:{of} \\ $$$${sinx}\:{and}\:{cosx}\:? \\ $$
Question Number 149296 Answers: 2 Comments: 0
$${if}\:\:\:{a}\:;\:{b}\:>\:\mathrm{0} \\ $$$${find}\:\:\:\left[\:\frac{\left({a}^{\mathrm{2}} \:+\:\mathrm{4}\right)\left({b}^{\mathrm{2}} \:+\:\mathrm{9}\right)}{{ab}}\:\right]_{\boldsymbol{{min}}} =\:? \\ $$
Question Number 149292 Answers: 1 Comments: 0
$${if}\:\:\:{sin}\mathrm{2}\boldsymbol{\alpha}\:=\:-\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${find}\:\:\:\mathrm{3}{tg}^{\mathrm{2}} \left(\frac{\mathrm{3}\boldsymbol{\pi}}{\mathrm{4}}\:-\:\boldsymbol{\alpha}\right)\:=\:? \\ $$
Question Number 149291 Answers: 2 Comments: 0
$${f}\left({x}\right)\:=\:\mathrm{2}{sinx}^{\mathrm{2}} −{cos}^{\mathrm{2}} {x}−\mathrm{2} \\ $$$${f}\:^{'} \left({x}\right)\:=\:? \\ $$
Question Number 152597 Answers: 0 Comments: 0
Question Number 149275 Answers: 0 Comments: 0
Question Number 149274 Answers: 1 Comments: 0
Question Number 149273 Answers: 3 Comments: 0
$$\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{\mathrm{e}^{\mathrm{tan}\:\mathrm{x}} \:\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}}\:\mathrm{dx}\:=? \\ $$
Question Number 149268 Answers: 4 Comments: 0
Question Number 149266 Answers: 1 Comments: 0
$${Solve}\:{for}\:{natural}\:{numbers}: \\ $$$${x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+{x}\:+\:{y}\:=\:\mathrm{3}{xy} \\ $$
Question Number 149271 Answers: 2 Comments: 0
Question Number 149259 Answers: 1 Comments: 0
$$\:\mathrm{cos}^{−\mathrm{1}} \left(\sqrt{\mathrm{sin}\:\left(\mathrm{41}°\right)\mathrm{sin}\:\left(\mathrm{19}°\right)+\frac{\mathrm{3}}{\mathrm{4}}}\:\right)=? \\ $$
Question Number 149252 Answers: 4 Comments: 0
$$ \\ $$$${e}^{{y}} =\left(\mathrm{sin}\:{x}\right)\left(\mathrm{cos}\:{x}\right) \\ $$$${find}\:\frac{{dy}}{{dx}} \\ $$
Question Number 149251 Answers: 2 Comments: 0
$$\:\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\frac{\mathrm{tan}\:\mathrm{x}\:\sqrt{\mathrm{tan}\:\mathrm{x}}−\mathrm{sin}\:\mathrm{x}\:\sqrt{\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\mathrm{3}} \:\sqrt{\mathrm{x}}}\:=? \\ $$$$ \\ $$
Question Number 149247 Answers: 0 Comments: 3
Question Number 149244 Answers: 0 Comments: 0
$$\:\:{Let}\:{a},{b},{c}\:{be}\:{positive}\:{real}\:{numbers} \\ $$$${with}\:{sum}\:\mathrm{3}.\:{Prove}\:{that}\: \\ $$$$\:\:\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{2}{a}^{\mathrm{2}} +{bc}}+\frac{\mathrm{3}}{\mathrm{2}{b}^{\mathrm{2}} +{ac}}+\frac{\mathrm{3}}{\mathrm{2}{c}^{\mathrm{2}} +{ab}} \\ $$
Question Number 149241 Answers: 2 Comments: 0
Question Number 149240 Answers: 1 Comments: 0
$$\:\:\mathrm{solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{number}\: \\ $$$$\:\mathrm{x}^{\mathrm{4}} −\mathrm{3x}^{\mathrm{2}} +\mathrm{1}\:=\sqrt{\frac{\mathrm{4}}{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }\:−\mathrm{1}} \\ $$$$\:\: \\ $$
Question Number 149239 Answers: 1 Comments: 0
$$\:\:\:\underset{{x}\rightarrow\mathrm{a}^{+} } {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}}−\sqrt{\mathrm{a}}\:−\sqrt{\mathrm{x}−\mathrm{a}}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} }}\:=?\: \\ $$
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