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Question Number 35151 Answers: 1 Comments: 0
Question Number 35150 Answers: 2 Comments: 0
Question Number 35139 Answers: 1 Comments: 2
Question Number 35136 Answers: 0 Comments: 1
Question Number 35131 Answers: 0 Comments: 2
Question Number 35127 Answers: 0 Comments: 0
$${Draw}\:{structure}\:{for} \\ $$$$\mathrm{2}-\left(\mathrm{4}-{Isobutylphenyl}\right){propanoic}\:{acid} \\ $$
Question Number 35117 Answers: 1 Comments: 0
$$\int\frac{\mathrm{2}{x}+\mathrm{3}}{{x}^{\mathrm{4}} −\mathrm{3}{x}−\mathrm{2}}{dx} \\ $$
Question Number 35124 Answers: 0 Comments: 9
Question Number 35115 Answers: 0 Comments: 2
Question Number 35101 Answers: 2 Comments: 1
$${Find}\:{volume}\:{enclosed}\:{by} \\ $$$$\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }+\frac{{z}^{\mathrm{2}} }{{c}^{\mathrm{2}} }=\mathrm{1}\:\:. \\ $$
Question Number 35092 Answers: 0 Comments: 0
Question Number 35088 Answers: 0 Comments: 2
$$\boldsymbol{{a}}\:\boldsymbol{{son}}\:\boldsymbol{{and}}\:\boldsymbol{{father}}\:\boldsymbol{{do}}\:\boldsymbol{{a}}\:\boldsymbol{{work}}\:\boldsymbol{{in}} \\ $$$$\mathrm{24}\:\boldsymbol{{day}}\:.\:\boldsymbol{{if}}\:\boldsymbol{{both}}\:\boldsymbol{{work}}\:\boldsymbol{{together}} \\ $$$$\boldsymbol{{and}}\:\boldsymbol{{father}}\:\boldsymbol{{work}}\:\boldsymbol{{last}}\:\mathrm{6}\:\boldsymbol{{day}}\:\boldsymbol{{only}} \\ $$$$\boldsymbol{{then}}\:\boldsymbol{{they}}\:\boldsymbol{{how}}\:\boldsymbol{{much}}\:\boldsymbol{{do}} \\ $$
Question Number 35084 Answers: 1 Comments: 1
Question Number 35080 Answers: 2 Comments: 0
$${If}\:\frac{{a}}{{b}+{c}}\:+\frac{{b}}{{c}+{a}}\:+\frac{{c}}{{a}+{b}}=\mathrm{1}\:{then}\:{prove}\:{that} \\ $$$$\frac{{a}^{\mathrm{2}} }{{b}+{c}}\:+\frac{{b}^{\mathrm{2}} }{{c}+{a}}\:+\frac{{c}^{\mathrm{2}} }{{a}+{b}}=\mathrm{0} \\ $$
Question Number 35072 Answers: 0 Comments: 2
$$\mathrm{An}\:\mathrm{n}-\mathrm{digit}\:\mathrm{decimal}\:\mathrm{number}\:\mathrm{has}\:\mathrm{been} \\ $$$$\mathrm{conveerted}\:\mathrm{into}\:\mathrm{octal}\:\mathrm{number}.\mathrm{Say}\:\mathrm{it} \\ $$$$\mathrm{has}\:\mathrm{m}\:\mathrm{digits}.\mathrm{What}\:\mathrm{are}\:\mathrm{possible}\:\:\mathrm{minimum}\: \\ $$$$\mathrm{and}\:\mathrm{maximum}\:\mathrm{values}\:\mathrm{of}\:\mathrm{m}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of} \\ $$$$\mathrm{n}? \\ $$
Question Number 35071 Answers: 1 Comments: 0
$$\mathrm{A}\:\mathrm{20}-\mathrm{digit}\:\mathrm{decimal}\:\mathrm{number}\:\mathrm{has}\:\mathrm{been} \\ $$$$\mathrm{converted}\:\mathrm{into}\:\mathrm{octal}\:\mathrm{system}.\mathrm{Say}\:\mathrm{it}\:\mathrm{has}\: \\ $$$$\mathrm{n}\:\mathrm{digits}.\:\mathrm{What}\:\mathrm{can}\:\mathrm{be}\:\mathrm{minimum}\:\mathrm{and} \\ $$$$\mathrm{maximum}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{n}? \\ $$$$ \\ $$
Question Number 35062 Answers: 0 Comments: 0
$${calculate}\:{A}_{{n}} \:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dt}}{\left({t}^{\mathrm{4}} \:+\mathrm{1}\right)^{{n}} } \\ $$$${with}\:{n}\:{integr}\:{natural}\:. \\ $$
Question Number 35061 Answers: 2 Comments: 1
$${find}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\frac{{x}^{\mathrm{2}} \:+\mathrm{3}}{\left({x}^{\mathrm{4}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$
Question Number 35060 Answers: 1 Comments: 1
$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{sinx}\:{ln}\left({cosx}\right){dx} \\ $$
Question Number 35059 Answers: 2 Comments: 2
$${find}\:\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\:\frac{{dx}}{{cosx}\:+{sinx}} \\ $$
Question Number 35058 Answers: 1 Comments: 1
$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\frac{{dt}}{\left(\mathrm{1}+{cos}^{\mathrm{2}} {t}\right)^{\mathrm{3}} } \\ $$
Question Number 35057 Answers: 0 Comments: 1
$${let}\:{u}_{{n}} =\left(\frac{{n}}{{n}+\mathrm{1}}\right)^{\frac{\mathrm{1}}{{n}}} \:\:−\mathrm{1} \\ $$$${find}\:{the}\:{nature}\:{of}\:\sum_{{n}\geqslant\mathrm{0}} {u}_{{n}} \\ $$
Question Number 35056 Answers: 0 Comments: 2
$${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{jx}\right)^{{n}} \:−\left(\mathrm{1}−{jx}\right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){factorize}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$${j}\:={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \:. \\ $$
Question Number 35055 Answers: 1 Comments: 2
$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} } \\ $$
Question Number 35054 Answers: 0 Comments: 1
$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\frac{{xdx}}{\mathrm{2}\:+{cosx}} \\ $$
Question Number 35053 Answers: 0 Comments: 0
$${let}\:{v}\left({x}\right)={ln}\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \right) \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$
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