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Question Number 48127 Answers: 1 Comments: 0
Question Number 48121 Answers: 0 Comments: 3
$${can}\:{the}\:{directrix}\:{of}\:{a}\:{parabola}\:{be}\:{in}\:{the}\:{form}\:{y}={mx}+{b}\:\:? \\ $$$${or}\:{is}\:{there}\:{an}\:{inclined}\:{parabola}\:{with}\:{directrix}\:{and}\:{axis}\: \\ $$$${of}\:{symmetry}\:{in}\:{the}\:{form}\:{of}\:{y}={mx}+{b}\:\:?? \\ $$
Question Number 48118 Answers: 0 Comments: 0
$$\sqrt{{a}^{\mathrm{2}} {x}^{\mathrm{2}} −{y}^{\mathrm{2}} }+\sqrt{{b}^{\mathrm{2}} {x}^{\mathrm{2}} −{y}^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\left({a}+{b}\right)\sqrt{\mathrm{2}{x}^{\mathrm{2}} +\frac{{x}^{\mathrm{4}} }{{x}^{\mathrm{4}} −{y}^{\mathrm{2}} }} \\ $$$${Find}\:{x}\:{such}\:{that}\:{y}\:{is}\:{minimum}. \\ $$$$\:\:{Assume}\:\:\:{x},\:{y}\:>\:\mathrm{0}\:. \\ $$
Question Number 48117 Answers: 0 Comments: 0
$${thanks}\:{sir} \\ $$
Question Number 48113 Answers: 2 Comments: 0
Question Number 48111 Answers: 1 Comments: 0
$$\left(−\mathrm{46}−×\right)/\left(−\mathrm{2}\right)=\mathrm{60}\:\: \\ $$$${hi}\:{sir}\:{plx}\:{help}\:{me} \\ $$
Question Number 48105 Answers: 1 Comments: 2
$$\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\:\left(\sqrt{\mathrm{1}+{x}+{x}^{\mathrm{2}} }−\:\sqrt{\mathrm{1}−{x}−{x}^{\mathrm{2}} }\:\right){dx}\:= \\ $$
Question Number 48104 Answers: 1 Comments: 0
$$\mathrm{solve}\:\mathrm{this}\:\: \\ $$$$\int\left(\mathrm{2}\:\mathrm{sinx}+\mathrm{cosx}\right)/\left(\mathrm{2}+\mathrm{3sinx}+\mathrm{sin}^{\mathrm{2x}} \right)\:\mathrm{dx} \\ $$
Question Number 48103 Answers: 0 Comments: 0
$$\mathrm{6} \\ $$
Question Number 48091 Answers: 1 Comments: 2
Question Number 48090 Answers: 1 Comments: 0
Question Number 48078 Answers: 1 Comments: 0
Question Number 48075 Answers: 1 Comments: 1
$$\mathrm{solve}\:\:\:\:\:\left(\mid{x}^{\mathrm{2}} −\mathrm{1}\mid−\frac{\mathrm{1}}{\mathrm{2}}\right){x}+\frac{\sqrt{\mathrm{6}}}{\mathrm{18}}=\mathrm{0} \\ $$
Question Number 48068 Answers: 1 Comments: 1
$${let}\:{u}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dt}}{\mathrm{1}+{t}^{{n}} } \\ $$$${find}\:{nature}\:{of}\:\Sigma\:{u}_{{n}} \:\:\:\:{and}\:\Sigma\:\frac{{u}_{{n}} }{{n}^{\mathrm{2}} }\:\:{and}\:\Sigma\:\frac{{u}_{{n}} }{{n}^{\mathrm{3}} } \\ $$
Question Number 48067 Answers: 0 Comments: 1
$${let}\:{y}>\mathrm{0}\:{give}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{{y}} }{{e}^{{x}} −\mathrm{1}}{dx}\:{at}\:{form}\:{of}\:{series}. \\ $$
Question Number 48066 Answers: 1 Comments: 4
$$\sqrt{\frac{\mathrm{1}}{\mathrm{2}}}.\sqrt{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\frac{\mathrm{1}}{\mathrm{2}}}}.\sqrt{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\frac{\mathrm{1}}{\mathrm{2}}}}}......\infty=? \\ $$
Question Number 48065 Answers: 0 Comments: 1
$$\left.{let}\:{f}\:\:\:\::\:\:\right]\mathrm{0},\mathrm{1}\left[\:\:{contnue}\:{integrable}\:\:{u}_{{n}} =\left(−\mathrm{1}\right)^{{n}} \:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{n}} {f}\left({x}\right){dx}\right. \\ $$$${prove}\:{that}\:\Sigma\:{u}_{{n}} \:{cnverge}\:{and}\:{find}\:{its}\:{sum} \\ $$$$ \\ $$
Question Number 48064 Answers: 1 Comments: 1
$${calculate}\:{A}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }{dx}\:\:−\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$
Question Number 48063 Answers: 0 Comments: 0
$${let}\:{W}\left({x}\right)\:=\int_{−\infty} ^{+\infty} \:\:\frac{{arctan}\left({xt}^{\mathrm{2}} \right)}{\mathrm{2}+{t}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{t}^{\mathrm{2}} }{\left(\mathrm{2}+{t}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} {t}^{\mathrm{4}} \right)}{dt}\:. \\ $$
Question Number 48062 Answers: 0 Comments: 0
$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{\left({x}^{\mathrm{2}} −\mathrm{3}\right){sin}\left(\mathrm{2}{x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }{dx} \\ $$
Question Number 48057 Answers: 2 Comments: 1
Question Number 48052 Answers: 2 Comments: 1
Question Number 48050 Answers: 1 Comments: 1
Question Number 48055 Answers: 2 Comments: 6
$${Solve}\:{the}\:{system}: \\ $$$$\begin{cases}{{x}^{\mathrm{3}} +{x}^{\mathrm{2}} {y}−\mathrm{4}{xy}^{\mathrm{2}} −\mathrm{4}{y}^{\mathrm{3}} =\mathrm{0}}\\{{x}^{\mathrm{2}} −\mathrm{2}{xy}−\mathrm{3}{y}^{\mathrm{2}} −{x}−{y}=\mathrm{0}}\end{cases} \\ $$
Question Number 48043 Answers: 0 Comments: 1
$${let}\:{f}\left(\alpha\right)\:=\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left(\alpha{x}^{\mathrm{3}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{8}}\:{dx} \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}\left(\alpha\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left(\mathrm{2}{x}^{\mathrm{3}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{8}}{dx}\:. \\ $$
Question Number 48042 Answers: 0 Comments: 1
$${find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{\mathrm{2}{x}+\mathrm{1}}{\left({x}^{\mathrm{2}} +{i}\right)\left({x}^{\mathrm{2}} +\mathrm{4}\right)}{dx}\:\:\:\left({i}^{\mathrm{2}} =−\mathrm{1}\right) \\ $$
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