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Question Number 90287 Answers: 1 Comments: 0
$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\begin{cases}{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{6}\:,\:\mathrm{x}\geqslant\mathrm{1}}\\{\mathrm{x}^{\mathrm{4}} +\mathrm{2x}^{\mathrm{3}} +\mathrm{2}\:,\mathrm{x}<\mathrm{1}}\end{cases} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{number}\: \\ $$$$\mathrm{c}\:\in\:\left(−\mathrm{2},\mathrm{3}\right)\:\mathrm{such}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{c}\right)\:=\:\mathrm{4} \\ $$
Question Number 90282 Answers: 0 Comments: 1
$$\frac{\mathrm{1}}{\mathrm{2}\alpha+\beta}+\frac{\mathrm{1}}{\alpha+\mathrm{2}\beta} \\ $$
Question Number 90281 Answers: 0 Comments: 2
$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt{\mathrm{x}}}{\left(\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{x}\right)\right)^{\mathrm{2}} }\:=\:? \\ $$
Question Number 90279 Answers: 0 Comments: 1
$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}\:{dx} \\ $$
Question Number 90272 Answers: 1 Comments: 0
Question Number 90262 Answers: 2 Comments: 2
$$\left(\mathrm{y}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\right)\:\mathrm{dx}\:=\:\mathrm{x}\:\mathrm{dy}\: \\ $$
Question Number 90259 Answers: 1 Comments: 0
$${a}\:{function}\:{f}\:{is}\:{defined}\:{on}\: \\ $$$${the}\:{positive}\:{integers}\:{satisfies}\: \\ $$$${f}\left(\mathrm{1}\right)\:=\:\mathrm{1002}\:,\:\&\:{f}\left(\mathrm{1}\right)+{f}\left(\mathrm{2}\right)+{f}\left(\mathrm{3}\right)+ \\ $$$$...\:+{f}\left({n}\right)\:=\:{n}^{\mathrm{2}} \:{f}\left({n}\right)\:. \\ $$$${find}\:{f}\left(\mathrm{2003}\right)\: \\ $$
Question Number 90258 Answers: 0 Comments: 1
Question Number 90256 Answers: 0 Comments: 0
$$\int_{\mathrm{0}} ^{\pi} \frac{{cos}\left(\mathrm{2}{x}\right)}{\left({e}^{{x}} +{cos}\left({x}\right)\right)^{\mathrm{2}} }{dx} \\ $$
Question Number 90252 Answers: 2 Comments: 1
Question Number 90251 Answers: 1 Comments: 2
$$\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} }{\mathrm{2}!}+\frac{\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} }{\mathrm{3}!}+.......=\:??? \\ $$
Question Number 90246 Answers: 0 Comments: 0
Question Number 90240 Answers: 0 Comments: 0
$${solve} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+{x}\frac{{dy}}{{dx}}+{xy}={x}^{\mathrm{3}} \\ $$$$ \\ $$
Question Number 90233 Answers: 0 Comments: 5
$$\mathrm{3},\mathrm{4},\mathrm{12},\mathrm{39},\mathrm{103},\mathrm{x}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{164} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{170} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{172} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{228} \\ $$
Question Number 90226 Answers: 0 Comments: 2
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{x}^{\mathrm{3}} \left({e}^{{x}} −\mathrm{1}\right)−{x}^{\mathrm{2}} }{{xe}^{{x}} −{x}}\right)=? \\ $$
Question Number 90225 Answers: 0 Comments: 3
$$\mathrm{x}+\mathrm{y}+\mathrm{z}\:=\:\mathrm{4} \\ $$$$\mathrm{z}+\mathrm{t}+\mathrm{x}\:=\:−\mathrm{3} \\ $$$$\mathrm{y}+\mathrm{z}+\mathrm{t}\:=\:\mathrm{4} \\ $$$$\mathrm{t}+\mathrm{x}+\mathrm{y}\:=\:\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} +\mathrm{t}^{\mathrm{2}} \: \\ $$
Question Number 90223 Answers: 0 Comments: 0
$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{12}\:\mathrm{books} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{put}\:\mathrm{in}\:\mathrm{3}\:\mathrm{shelves},\:\mathrm{4}\:\mathrm{on}\:\mathrm{each},\:\mathrm{is} \\ $$
Question Number 90222 Answers: 0 Comments: 1
Question Number 90220 Answers: 0 Comments: 0
$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{8}\:\mathrm{distinct} \\ $$$$\mathrm{toys}\:\mathrm{can}\:\mathrm{be}\:\mathrm{distributed}\:\mathrm{among}\:\mathrm{5}\: \\ $$$$\mathrm{children}\:\mathrm{is} \\ $$
Question Number 90221 Answers: 0 Comments: 0
$$\mathrm{There}\:\mathrm{are}\:\mathrm{3}\:\mathrm{copies}\:\mathrm{each}\:\mathrm{of}\:\mathrm{4}\:\mathrm{different} \\ $$$$\mathrm{books}.\:\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which} \\ $$$$\mathrm{in}\:\mathrm{which}\:\mathrm{they}\:\mathrm{can}\:\mathrm{be}\:\mathrm{arranged}\:\mathrm{in}\:\mathrm{a}\: \\ $$$$\mathrm{shelf}\:\mathrm{is} \\ $$
Question Number 90217 Answers: 0 Comments: 2
$${let}\:{x}_{{n}\:} \:{be}\:{a}\:{sequence}\:{with}\:{x}_{\mathrm{0}} =\mathrm{2}\:{and}\:{x}_{\mathrm{1}} =\mathrm{7} \\ $$$${and}\:{x}_{{n}+\mathrm{1}} =\mathrm{7}{x}_{{n}} −\mathrm{12}{x}_{{n}−\mathrm{1}} . \\ $$$${Find}\:{the}\:{general}\:{term}\:{of}\:{x}_{{n}} . \\ $$
Question Number 90212 Answers: 0 Comments: 4
$${if}\:{x}^{\mathrm{2}} \:=\:\mathrm{5}{x}+\mathrm{1}\: \\ $$$${find}\:{E}\:=\:\frac{\left({x}^{\mathrm{3}} −\mathrm{140}\right)\:\sqrt[{\mathrm{3}\:\:}]{{x}^{\mathrm{11}} }}{\sqrt[{\mathrm{3}\:\:}]{{x}^{\mathrm{4}} +\mathrm{1}}} \\ $$
Question Number 90210 Answers: 1 Comments: 1
$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}−\mathrm{2cos}\:\left({x}\right)}{\pi−\mathrm{3}{x}}\right)=? \\ $$
Question Number 90208 Answers: 0 Comments: 0
Question Number 90200 Answers: 0 Comments: 7
$$\mathrm{26}\equiv\mathrm{R}_{\mathrm{1}} \left[\mathrm{37}\right] \\ $$$$\mathrm{1}\:\:\equiv\mathrm{R}_{\mathrm{2}} \left[\mathrm{3}\right] \\ $$$$\mathrm{2}\equiv\mathrm{R}_{\mathrm{3}} \left[\mathrm{5}\right] \\ $$$$\mathrm{Find}\:\mathrm{R}_{\mathrm{1}} ,\:\mathrm{R}_{\mathrm{2}} \mathrm{and}\:\mathrm{R}_{\mathrm{3}} \\ $$
Question Number 90198 Answers: 3 Comments: 3
$$\int{sin}\left({dx}\right)\: \\ $$
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