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Question Number 74019 Answers: 1 Comments: 3
$${let}\:{the}\:{matrix}\:\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:−\mathrm{3}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{{n}} \:\:{for}\:{n}\:{integr} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{e}^{{A}} \:\:{and}\:{e}^{−{A}} . \\ $$
Question Number 74017 Answers: 0 Comments: 3
$${let}\:{f}\left({x}\right)=\int_{{x}} ^{{x}^{\mathrm{2}} +\mathrm{3}} \:{e}^{−{xt}} \:{ln}\left(\mathrm{1}+{e}^{−{xt}} \right){dt}\:\:\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right). \\ $$
Question Number 74016 Answers: 1 Comments: 5
$${let}\:{g}\left({x}\right)\:=\frac{\mathrm{1}}{{x}}\int_{{x}} ^{\mathrm{2}{x}+\mathrm{1}} \:\:{arctan}\left({xt}\right){dt} \\ $$$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:{g}\left({x}\right)\:\:{and}\:{lim}_{{x}\rightarrow+\infty} {g}\left({x}\right). \\ $$
Question Number 74015 Answers: 0 Comments: 1
$${let}\:{f}\left({x}\right)\:=\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\:\frac{{sh}\left({xt}\right)}{{sin}\left({xt}\right)}{dt} \\ $$$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} {f}\left({x}\right) \\ $$
Question Number 74014 Answers: 0 Comments: 1
$$\:\: \\ $$$$\:\:{let}\:{W}\left({x}\right)=\sum_{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} \:\:\frac{{x}^{{i}+{j}} }{{ij}} \\ $$$${calculate}\:{W}\:^{'} \left({x}\right). \\ $$
Question Number 74013 Answers: 1 Comments: 3
$${let}\:\:\:{P}\left({x}\right)=\:\sum_{\mathrm{0}\leqslant{i}<{j}\leqslant{n}} \:{x}^{{i}+{j}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{P}\:^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{P}\left({x}\right){dx} \\ $$
Question Number 74000 Answers: 1 Comments: 0
$${if}\:{p}_{{r}} ^{{n}} =\mathrm{840}\:,\:{c}_{{r}} ^{{n}} =\mathrm{35}\:{find}\:{value}\:{of}\:{r}? \\ $$$${pleas}\:{sir}\:{help}\:{me}? \\ $$
Question Number 74006 Answers: 1 Comments: 1
$${If}\:\mathrm{3}{x}^{\mathrm{2}} {e}^{\mathrm{log}\:_{{x}} \mathrm{27}} =\mathrm{27000}\:{then}\:{find}\:{x} \\ $$
Question Number 74005 Answers: 0 Comments: 0
$${find}\:{C}_{\mathrm{8}} ^{\mathrm{15}} +{C}_{\mathrm{9}} ^{\mathrm{15}} −{C}_{\mathrm{7}} ^{\mathrm{15}} −{C}_{\mathrm{6}} ^{\mathrm{15}} \:? \\ $$$${pleas}\:{help}\:{me}\:{sir}\:? \\ $$
Question Number 74003 Answers: 0 Comments: 1
Question Number 73983 Answers: 2 Comments: 0
$${if}\:{p}_{{r}} ^{{n}} =\mathrm{49}\:,\:{c}_{{r}} ^{{n}} =\mathrm{196}\:{find}\:{the}\:{valve}\:{of}\:{r}\:{and}\:{n}? \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$
Question Number 73982 Answers: 0 Comments: 2
Question Number 73974 Answers: 1 Comments: 0
$$\mathrm{Prove}\:\mathrm{this}\:\mathrm{equation} \\ $$$$\frac{\mathrm{2}^{{x}−\mathrm{1}} \left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)!}{\frac{\mathrm{1}}{\mathrm{2}}!}=\frac{\left(\mathrm{2}{x}−\mathrm{1}\right)!}{\mathrm{2}^{{x}−\mathrm{1}} \left({x}−\mathrm{1}\right)!} \\ $$
Question Number 73964 Answers: 2 Comments: 0
$${if}\:{Im}\left({f}\:'\left({z}\right)\right)\:=\mathrm{6}{x}\left(\mathrm{2}{y}−\mathrm{1}\right)\:{and}\: \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{3}−\mathrm{2}{i}\:,\:{f}\left(\mathrm{1}\right)=\mathrm{6}−\mathrm{5}{i}\: \\ $$$${find}\:{f}\left(\mathrm{1}+{i}\right)? \\ $$
Question Number 73948 Answers: 2 Comments: 1
$${lim}\:\:\:\left(\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}}{{x}}\right) \\ $$$${x}\rightarrow\mathrm{0} \\ $$
Question Number 73940 Answers: 1 Comments: 0
Question Number 73913 Answers: 2 Comments: 0
$${I}\:{need}\:{the}\:{sol}.\:{plz} \\ $$$${find}\:{the}\:{imaginary}\:{and}\:{real}\:{parts}\:{of} \\ $$$${log}\:{sin}\left({a}+{ib}\right)? \\ $$
Question Number 73910 Answers: 0 Comments: 6
Question Number 73909 Answers: 2 Comments: 1
Question Number 73901 Answers: 2 Comments: 0
Question Number 73896 Answers: 2 Comments: 1
Question Number 73918 Answers: 2 Comments: 2
$${find}\:{the}\:{Re}\left({w}\right)\:{and}\:{Im}\left({w}\right) \\ $$$$ \\ $$$${where}\:{w}\:=\:\left({sin}\:{a}\:+\:{icos}\:{a}\right)^{\left({cos}\:{a}\:+\:{isin}\:{a}\right)} \\ $$
Question Number 73884 Answers: 0 Comments: 0
Question Number 73872 Answers: 1 Comments: 0
Question Number 73847 Answers: 0 Comments: 4
Question Number 73919 Answers: 1 Comments: 3
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