Question Number 91268 by mathmax by abdo last updated on 29/Apr/20 $${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{1}\:\:\:\:\:−\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculste}\:{A}^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:\:{e}^{{A}} \:\:{and}\:{e}^{−\mathrm{2}{A}} \\ $$$$\left.\mathrm{3}\right){find}\:{cos}\left({A}\right){and}\:{sinA}\:\:\:{is}\:{cos}^{\mathrm{2}} {A}\:+{sin}^{\mathrm{2}} {A}\:={I}? \\ $$$$\left.\mathrm{4}\right)\:{determine}\:{sh}\left({A}\right)\:{and}\:{ch}\left({A}\right)\:\:{is}\:{ch}^{\mathrm{2}} {A}−{sh}^{\mathrm{2}} {A}\:={I}\:\:?…
Question Number 156793 by alcohol last updated on 15/Oct/21 $$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{sin}\mathrm{2}{x}}{\mathrm{2}−{sin}^{\mathrm{2}} \mathrm{2}{x}}{dx} \\ $$ Answered by FongXD last updated on 15/Oct/21 $$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin2x}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}}…
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Question Number 91085 by jagoll last updated on 28/Apr/20 $${f}\left({x}\right)\:=\:\lceil\mathrm{2}{x}−\mathrm{1}\rceil\: \\ $$$${f}\left(\mathrm{3}\right)\:,\:{f}\left(\mathrm{4}\right)\:=\:? \\ $$ Commented by M±th+et+s last updated on 28/Apr/20 $${if}\:\left[…\right]\:{is}\:{ceil} \\ $$$${f}\left(\mathrm{3}\right)=\lceil\mathrm{6}−\mathrm{1}\rceil=\lceil\mathrm{5}\rceil=\mathrm{5} \\…
Question Number 90973 by abdomathmax last updated on 27/Apr/20 $${solve}\:{xy}^{'} \:+\left({x}+\mathrm{1}\right){y}\:={e}^{−{x}} {ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right) \\ $$ Commented by mathmax by abdo last updated on 27/Apr/20 $$\left({he}\right)\rightarrow{xy}^{'}…
Question Number 90972 by abdomathmax last updated on 27/Apr/20 $${solve}\:{y}^{''} \:+{y}\:=\frac{\mathrm{2}}{{sin}^{\mathrm{2}} {t}} \\ $$ Answered by Joel578 last updated on 27/Apr/20 $$\bullet\:\mathrm{Homogeneous}\:\mathrm{solution} \\ $$$$\mathrm{with}\:\mathrm{char}.\:\mathrm{eq}.\:\lambda^{\mathrm{2}} \:+\:\mathrm{1}\:=\:\mathrm{0}\:\rightarrow\:\lambda_{\mathrm{1},\mathrm{2}}…
Question Number 90971 by abdomathmax last updated on 27/Apr/20 $${solve}\:{y}^{''} \:+{y}^{'} \:+{y}\:=\frac{{e}^{−{t}} }{{ch}^{\mathrm{2}} {t}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 90970 by abdomathmax last updated on 27/Apr/20 $${find}\:{all}\:{functions}\:{f}\:\:\left(\mathrm{2}×{derivable}\right)\:{verify} \\ $$$$\left({f}^{'} \left({x}\right)\right)^{\mathrm{2}} \:−\left({f}\left({x}\right)\right)^{\mathrm{2}} \:=\mathrm{1}\:{and}\:{f}^{'} \left(\mathrm{0}\right)=\mathrm{1} \\ $$ Commented by mr W last updated on…
Question Number 90969 by abdomathmax last updated on 27/Apr/20 $${solve}\:{y}^{''} −\mathrm{2}{ay}^{'} \:+\left(\mathrm{1}+{a}^{\mathrm{2}} \right){y}\:={x}\:+{e}^{{ax}} \\ $$$${a}\:{real} \\ $$ Commented by niroj last updated on 27/Apr/20 $$\:\mathrm{y}^{''}…
Question Number 90968 by abdomathmax last updated on 27/Apr/20 $${solve}\:\left(\mathrm{1}+{e}^{{x}} \right){y}^{'} −{y}\:=\frac{{e}^{{x}} }{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$ Commented by niroj last updated on 27/Apr/20 $$\:\:\:\:\left(\mathrm{1}+\mathrm{e}^{\mathrm{x}} \right)\mathrm{y}^{'}…