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Question Number 67860 Answers: 1 Comments: 3
Question Number 67852 Answers: 1 Comments: 4
Question Number 67851 Answers: 0 Comments: 5
$${find}\:\int\:\:\frac{{dx}}{{x}^{\mathrm{2}} −{z}}\:\:{with}\:{z}\:{from}\:{C}\:. \\ $$
Question Number 67850 Answers: 0 Comments: 1
$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} −{z}}\:\:{with}\:{z}\:{from}\:{C} \\ $$
Question Number 67849 Answers: 1 Comments: 7
Question Number 67844 Answers: 0 Comments: 2
$${x}^{\mathrm{2}} +\mid{x}\mid−\mathrm{6}=\mathrm{0} \\ $$
Question Number 67836 Answers: 0 Comments: 0
$$\mathrm{If}\:\begin{vmatrix}{{x}^{{n}} }&{{x}^{{n}+\mathrm{2}} }&{{x}^{{n}+\mathrm{3}} }\\{{y}^{{n}} }&{{y}^{{n}+\mathrm{2}} }&{{y}^{{n}+\mathrm{3}} }\\{{z}^{{n}} }&{{z}^{{n}+\mathrm{2}} }&{{z}^{{n}+\mathrm{3}} }\end{vmatrix} \\ $$$$=\:\left({x}−{y}\right)\left({y}−{z}\right)\left({z}−{x}\right)\left(\frac{\mathrm{1}}{{x}}\:+\:\frac{\mathrm{1}}{{y}}\:+\:\frac{\mathrm{1}}{{z}}\right), \\ $$$$\mathrm{then}\:{n}\:\mathrm{equals} \\ $$
Question Number 67835 Answers: 1 Comments: 0
$$\int_{\mathrm{0}} ^{\mathrm{2}} {x}\left(\mathrm{8}−{x}^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} {dx} \\ $$
Question Number 67826 Answers: 2 Comments: 4
Question Number 67823 Answers: 0 Comments: 0
$$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{lnx}+{e}^{{lnx}/{x}} } {dx} \\ $$
Question Number 67820 Answers: 0 Comments: 1
$${x}^{\mathrm{3}} −{x}^{\mathrm{2}} −\mathrm{6}{x} \\ $$
Question Number 67819 Answers: 0 Comments: 1
$${y}={x}^{\mathrm{5}} +{ax}^{\mathrm{4}} +{bx}^{\mathrm{3}} +{cx}^{\mathrm{2}} +{dx}+{e} \\ $$$${If}\:{we}\:{let}\:{x}={t}+{h} \\ $$$${can}\:{we}\:{find}\:{h}\:{in}\:{terms}\:{of}\:{a},{b},{c},{d},{e} \\ $$$${such}\:{that} \\ $$$${y}=\left({t}+{R}\right)\left({t}^{\mathrm{2}} +{pt}+{q}\right)\left({t}^{\mathrm{2}} +{s}\right) \\ $$$${this}\:{means}\:{two}\:{roots}\:{are}\:{of} \\ $$$${opposite}\:{sign},\:{of}\:{course}\:{its} \\ $$$${possible}\:{by}\:{shifting}\:{the}\:{curve} \\ $$$${along}\:{x},\:{but}\:{can}\:{we}\:{find}\:{the} \\ $$$${shift}\:\boldsymbol{{h}}\:? \\ $$
Question Number 67807 Answers: 1 Comments: 2
Question Number 67799 Answers: 1 Comments: 3
$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:−{e}^{{ia}} \right)\left({x}^{\mathrm{2}} −{e}^{{ib}} \right)}\:\:{with}\:{a}>\mathrm{0}\:{andb}>\mathrm{0} \\ $$
Question Number 67795 Answers: 0 Comments: 2
$${let}\:\:{A}_{{p}} =\int_{\mathrm{0}} ^{\pi} \:{x}^{{p}} \:{cos}\left({nx}\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{0}} ,{A}_{\mathrm{1}} ,{A}_{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right){determine}\:{a}\:{relation}\:{of}\:{recurrence}\:{between}\:\:{A}_{{p}} \\ $$
Question Number 67775 Answers: 2 Comments: 0
Question Number 67774 Answers: 1 Comments: 0
Question Number 67772 Answers: 2 Comments: 3
Question Number 67770 Answers: 1 Comments: 0
Question Number 67813 Answers: 1 Comments: 8
Question Number 67760 Answers: 0 Comments: 0
$${y}'={y}^{\mathrm{2}} +\mathrm{2}\:;\:{y}\left(\mathrm{0}\right)=\mathrm{2} \\ $$$$ \\ $$$${solve}\:{by}\:{picards}\:{iteration}\:{method} \\ $$$$ \\ $$
Question Number 67759 Answers: 0 Comments: 1
$${using}\:{variation}\:{of}\:{parameters}\:{method} \\ $$$$ \\ $$$$\left({x}+\mathrm{2}\right)^{\mathrm{2}} {y}''−\left({x}+\mathrm{2}\right){y}'=\mathrm{2}{x}+\mathrm{4} \\ $$$$ \\ $$$$ \\ $$$${x}^{\mathrm{2}} {y}''+\mathrm{2}{xy}'−\mathrm{2}{y}={x}^{\mathrm{2}} {lnx}+\mathrm{3}{x} \\ $$
Question Number 67761 Answers: 0 Comments: 0
$${solve}\:{by}\:{laplace}\:{transform}\:{method} \\ $$$$ \\ $$$$\overset{\bullet\bullet\:} {{x}}\:+{w}_{\mathrm{0}} ^{\mathrm{2}} {x}={coswt}\:\:\:{x}\left(\mathrm{0}\right)={x}_{\mathrm{0}} \:\overset{\bullet} {{x}}\left(\mathrm{0}\right)={v}_{\mathrm{0}} \:\:\:\:\:{w}^{\mathrm{2}} \neq\:{w}_{\mathrm{0}} ^{\mathrm{2}} \\ $$
Question Number 67762 Answers: 0 Comments: 0
$${solve}\:{by}\:{the}\:{complex}\:{method} \\ $$$$ \\ $$$$ \\ $$$${y}^{{iv}} +\mathrm{3}{y}^{\mathrm{3}} +\mathrm{2}{y}^{\mathrm{2}} =−\mathrm{3}{sin}\mathrm{2}{x} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$${y}^{\mathrm{2}} +{a}^{\mathrm{2}} {y}={e}^{{x}} {cosecx} \\ $$
Question Number 67749 Answers: 1 Comments: 0
Question Number 67745 Answers: 3 Comments: 0
$${solve}\:{the}\:{system}\:{of}\:{equations\begin{cases}{\mathrm{3}\mid{x}−\mathrm{5}\mid+\mathrm{4}={y}}\\{\mid{y}−\mathrm{3}\mid=\mathrm{4}{x}−\mathrm{12}}\end{cases}} \\ $$
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