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Question Number 103093 Answers: 5 Comments: 0
$${solve}\:{for}\:{x},{y}\in\mathbb{N} \\ $$$$\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}=\frac{\mathrm{3}}{\mathrm{202}} \\ $$
Question Number 102980 Answers: 1 Comments: 6
Question Number 102978 Answers: 2 Comments: 1
Question Number 102975 Answers: 0 Comments: 1
$$\mathrm{A}\:\mathrm{student}\:\mathrm{can}\:\mathrm{recall}\:\mathrm{6}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{a}\:\mathrm{9}\:\mathrm{digit}\:\mathrm{number}. \\ $$$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{he}\:\mathrm{get}\:\mathrm{the}\:\mathrm{complete}\:\mathrm{number}? \\ $$
Question Number 102967 Answers: 1 Comments: 0
Question Number 102944 Answers: 0 Comments: 5
Question Number 102940 Answers: 0 Comments: 1
Question Number 102927 Answers: 3 Comments: 1
$$\mathrm{If}\:\:\:\frac{\mathrm{x}}{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{x}\:\:+\:\:\mathrm{1}}\:\:\:=\:\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{Find}\:\:\:\:\:\mathrm{x}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{x}} \\ $$
Question Number 102926 Answers: 3 Comments: 0
$$\:\int\:\frac{{d}\theta}{\mathrm{2}{sin}^{\mathrm{2}} \theta−{cos}^{\mathrm{2}} \theta}\:\:? \\ $$
Question Number 102922 Answers: 1 Comments: 1
$$\int\:\frac{{dx}}{{x}^{\mathrm{3}} +\mathrm{3}{x}−\mathrm{5}}\:\:? \\ $$
Question Number 103071 Answers: 0 Comments: 0
$$\int\frac{\mathrm{e}^{\mathrm{x}} }{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\centerdot\left(\mathrm{x}^{\mathrm{3}} −\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)\mathrm{dx} \\ $$
Question Number 102918 Answers: 1 Comments: 2
Question Number 102911 Answers: 2 Comments: 1
$$\int\:\frac{\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{x}}\:\:\mathrm{dx} \\ $$
Question Number 102910 Answers: 1 Comments: 0
$$\left(\mathrm{1}\right)\underset{\mathrm{m}\:=\:\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{m}\pi}{\mathrm{2n}+\mathrm{1}}\right) \\ $$$$\left(\mathrm{2}\right)\:\underset{\mathrm{m}\:=\:\mathrm{1}} {\overset{\mathrm{n}} {\prod}}\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{m}\pi}{\mathrm{2n}+\mathrm{1}}\right)\: \\ $$
Question Number 102905 Answers: 1 Comments: 0
$${I}=\mathrm{2}\underset{\mathrm{0}} {\overset{\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}} {\int}}\:\frac{\mathrm{sin}^{−\mathrm{1}} \left({x}\right)}{{x}}\:{dx}\:−\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{tan}^{−\mathrm{1}} \left({x}\right)}{{x}}{dx} \\ $$
Question Number 102880 Answers: 1 Comments: 5
Question Number 102963 Answers: 0 Comments: 0
Question Number 102857 Answers: 0 Comments: 1
Question Number 102854 Answers: 1 Comments: 0
Question Number 102883 Answers: 1 Comments: 0
$${If}\:{x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c}\:=\:\mathrm{0}\:{has}\:{the}\:{roots}\:{are}\: \\ $$$$\bar {\alpha}\:\beta\:{and}\:\gamma\:.\:{find}\:{the}\:{value}\:{of} \\ $$$$\alpha\beta^{\mathrm{2}} +\beta\gamma^{\mathrm{2}} +\gamma\alpha^{\mathrm{2}} \:{in}\:{terms}\:{a},{b}\:{and}\:{c} \\ $$
Question Number 102843 Answers: 0 Comments: 8
Question Number 102840 Answers: 1 Comments: 0
$${y}'+\sqrt{{x}+{y}−\mathrm{1}}={x}+{y}+\mathrm{1} \\ $$
Question Number 102838 Answers: 1 Comments: 2
Question Number 102836 Answers: 2 Comments: 1
Question Number 102822 Answers: 1 Comments: 1
$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}!}{{n}^{{n}} } \\ $$
Question Number 102819 Answers: 0 Comments: 4
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