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Question Number 49748 Answers: 1 Comments: 0
Question Number 49661 Answers: 1 Comments: 2
$${calculateA}_{{n}} =\frac{\mathrm{1}}{\mathrm{2}{i}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \left\{\left(\mathrm{1}+{ix}\right)^{{n}} −\left(\mathrm{1}−{ix}\right)^{{n}} \right\}{dx} \\ $$
Question Number 49660 Answers: 2 Comments: 1
Question Number 49647 Answers: 1 Comments: 3
$${let}\:{p}\left({x}\right)\:={x}^{\mathrm{2}{n}} \:−{x}^{{n}} \:+\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{inside}\:{C}\left[{x}\right]\:{the}\:{polynom}\:{p}\left({x}\right)\:. \\ $$$$\left.\mathrm{3}\right){solve}\:{p}\left({x}\right)=\mathrm{0}\:\:{and}\:{p}\left({x}\right)\:=\mathrm{2} \\ $$
Question Number 49646 Answers: 0 Comments: 0
$${calculate}\:\int\int_{{D}} \left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)\sqrt{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{dxdy}\:{with} \\ $$$${D}\:=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\:−\mathrm{1}\leqslant{x}\leqslant\mathrm{1}\:{and}\:\mathrm{0}\leqslant{y}\leqslant\mathrm{2}\:\right\} \\ $$
Question Number 49645 Answers: 1 Comments: 0
$${calculate}\:\int\int_{{C}} \:\mid{x}+{y}\mid{dxdy}\:\:{with}\:{C}=\left[−\mathrm{1},\mathrm{1}\right]×\left[−\mathrm{1},\mathrm{1}\right] \\ $$
Question Number 70360 Answers: 1 Comments: 0
$$\underset{{n}\rightarrow+\infty} {\mathrm{l}im}\:\:\:\:\frac{\sqrt{{n}\:+\:\mathrm{1}\:}−\:{n}}{\sqrt{{n}\:+\:\mathrm{1}}\:+\:{n}}\:\:=\:\:? \\ $$
Question Number 49642 Answers: 1 Comments: 0
$${if}\:\:{a}+{b}\:={s}\:{and}\:{a}^{\mathrm{3}} \:+{b}^{\mathrm{3}} \:={t}\:\:{find}\:{a}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \:\:{and}\:{a}^{\mathrm{4}} \:+{b}^{\mathrm{4}} \:{interms}\:{of}\:{s}\:{and}\:{t}\:. \\ $$
Question Number 49640 Answers: 1 Comments: 2
$${if}\:{x}\:\in\left[{p},\sqrt{{p}^{\mathrm{2}} \:+\mathrm{2}}\right]\:\:{calculate}\:\left[{x}\right] \\ $$
Question Number 49639 Answers: 1 Comments: 1
$${find}\:{a}\:{relation}\:{betwen}\:\left[{x}\right]^{\mathrm{2}} \:{and}\:\left[−{x}\right]^{\mathrm{2}} \\ $$
Question Number 49638 Answers: 1 Comments: 0
$${let}\:{a}>\mathrm{2}\:{and}\:{f}\left({a}\right)\:=\int_{−\frac{\mathrm{1}}{{a}}} ^{\frac{\mathrm{1}}{{a}}} \:\:\:\frac{{x}^{\mathrm{2}} {dx}}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right)\:{interms}\:{of}\:{a} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({a}\right)\:. \\ $$
Question Number 49637 Answers: 1 Comments: 0
Question Number 49636 Answers: 1 Comments: 2
$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{n}\left[{x}\right]} {sin}\left({x}\right){dx}\:{with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{A}_{{n}} \\ $$
Question Number 49635 Answers: 1 Comments: 1
$$\left.\mathrm{1}\right){find}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{sint}}{\mathrm{2}+{x}\:{cos}\left(\mathrm{2}{t}\right)}{dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{sint}\:{sin}\left(\mathrm{2}{t}\right.}{\left(\mathrm{2}+{x}\:{cos}\left(\mathrm{2}{t}\right)\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\frac{{sint}}{\mathrm{2}+\mathrm{3}\:{cos}\left(\mathrm{2}{t}\right)}{dt}\:\:{and}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{{sin}\left({t}\right){sin}\left(\mathrm{2}{t}\right)}{\left(\mathrm{2}+\mathrm{3}{cos}\left(\mathrm{2}{t}\right)\right)^{\mathrm{2}} }{dt} \\ $$
Question Number 49621 Answers: 0 Comments: 0
Question Number 49605 Answers: 1 Comments: 3
Question Number 49604 Answers: 2 Comments: 0
$$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\:\:\:\:\:\:\:\frac{\left(\mathrm{a}\:+\:\mathrm{b}\right)^{\mathrm{2}} }{\mathrm{2}}\:\:\leqslant\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \\ $$
Question Number 49602 Answers: 0 Comments: 0
$$\varnothing=\mathrm{0} \\ $$
Question Number 71170 Answers: 1 Comments: 1
Question Number 49594 Answers: 0 Comments: 1
$$\:\:\:\:{How}\:{can}\:{we}\:{insert}\:{images}\:{in}\:{the}\:{editor}? \\ $$
Question Number 49651 Answers: 0 Comments: 3
Question Number 49570 Answers: 1 Comments: 0
$$\mathrm{Eliminate}\:\:\boldsymbol{\mathrm{t}}\:\:\mathrm{from}\:\mathrm{this}\:\mathrm{equation}:\:\:\left(\mathrm{1}\right)\:\:\:\mathrm{x}\:=\:\mathrm{1}\:+\:\mathrm{t},\:\:\:\mathrm{y}\:=\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{t}} \\ $$$$\left(\mathrm{2}\right)\:\:\mathrm{x}\:=\:\mathrm{3}\:+\:\mathrm{t}^{\mathrm{3}} \:,\:\:\:\:\:\mathrm{y}\:=\:\mathrm{2}\:+\:\frac{\mathrm{1}}{\mathrm{t}} \\ $$
Question Number 51422 Answers: 2 Comments: 1
Question Number 49559 Answers: 2 Comments: 1
Question Number 49555 Answers: 0 Comments: 0
$$\mathrm{Find}\:\mathrm{4}\:\: \\ $$$$\mathrm{plz}\:\mathrm{help}\:\mathrm{me}\:\mathrm{sir} \\ $$
Question Number 49554 Answers: 0 Comments: 0
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