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Question Number 85346 Answers: 1 Comments: 1
$$\underset{\:\mathrm{0}} {\int}\:\overset{\infty} {\:}\:\:\frac{\mathrm{cos}\:\left(\pi{x}\right)}{\pi^{\mathrm{2}} +{x}^{\mathrm{2}} }\:{dx}\:\:=\:\:? \\ $$
Question Number 85372 Answers: 1 Comments: 0
$$\mathrm{sin}\:^{\mathrm{2}} {x}−\mathrm{4cos}\:^{\mathrm{2}} {x}\:=\:\mathrm{3}\:\mathrm{sin}\:{x}\:\mathrm{cos}\:{x} \\ $$$${find}\:\mathrm{tan}\:{x}.\: \\ $$
Question Number 85374 Answers: 0 Comments: 2
$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{7}} +{x}^{\mathrm{3}} +\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}\:{dx}\: \\ $$
Question Number 85323 Answers: 1 Comments: 0
$$\int\frac{\mathrm{z}−\mathrm{3}}{\mathrm{5z}−\mathrm{10}}\mathrm{dz} \\ $$
Question Number 85321 Answers: 0 Comments: 0
Question Number 85322 Answers: 0 Comments: 10
$${please}\:{help}\:{me}\:{to}\:{solve}\:{this}\:{in}\:\mathbb{N} \\ $$$${A}_{{n}} ^{\mathrm{2}} −\mathrm{3}{C}_{{n}} ^{\:{n}−\mathrm{2}} +{n}=−\mathrm{20} \\ $$
Question Number 85319 Answers: 1 Comments: 0
$$\int\frac{\mathrm{2}+\mathrm{u}}{−\mathrm{u}^{\mathrm{2}} −\mathrm{u}}\mathrm{du} \\ $$
Question Number 85318 Answers: 0 Comments: 1
Question Number 85315 Answers: 0 Comments: 1
$$\mathrm{The}\:\mathrm{largest}\:\mathrm{interval}\:\mathrm{in}\:\mathrm{which}\:{x}\:\mathrm{lies} \\ $$$$\mathrm{satisfying}\:{x}^{\mathrm{12}} −{x}^{\mathrm{9}} +{x}^{\mathrm{4}} −{x}+\mathrm{1}>\mathrm{0}\:\mathrm{is} \\ $$
Question Number 85313 Answers: 1 Comments: 0
$$\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{20}^{\mathrm{o}} \right)\:+\:\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{40}^{\mathrm{o}} \right)+\:\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{80}^{\mathrm{o}} \right)\:= \\ $$
Question Number 85298 Answers: 2 Comments: 2
$${Find}\:{the}\:{symmetry}\:{axes}\:\left({if}\:{any}\right)\:{of} \\ $$$${the}\:{following}\:{curve}: \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{xy}+\mathrm{2}{x}−\mathrm{8}{y}−\mathrm{2}=\mathrm{0} \\ $$
Question Number 85293 Answers: 2 Comments: 1
$$\underset{{x}\rightarrow\mathrm{0}^{+} \:} {\mathrm{lim}}\:\sqrt{\frac{\mathrm{1}}{\mathrm{x}}}−\sqrt{\frac{\mathrm{1}}{\mathrm{2x}}−\mathrm{2020}}\:? \\ $$
Question Number 85286 Answers: 0 Comments: 2
Question Number 85280 Answers: 1 Comments: 0
$$\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{cot}^{−\mathrm{1}} \left(\mathrm{1}−{x}+{x}^{\mathrm{2}} \right)\:{dx}\:= \\ $$
Question Number 85279 Answers: 3 Comments: 0
$$\mathrm{who}\:\mathrm{can}\:\mathrm{help}\:\mathrm{write}\:\mathrm{out}\:\mathrm{the}\:\mathrm{mechanism}\:\mathrm{for}\:\mathrm{the}\: \\ $$$$\mathrm{reaction} \\ $$$$\:\:\:\mathrm{C}_{\mathrm{6}} \mathrm{H}_{\mathrm{6}} \:\underset{\mathrm{HNO}_{\mathrm{3}} } {\overset{\mathrm{H}_{\mathrm{2}} \mathrm{SO}_{\mathrm{4}} } {\rightarrow}}\:\:\mathrm{C}_{\mathrm{6}} \mathrm{H}_{\mathrm{5}} \mathrm{NO}_{\mathrm{2}} \\ $$
Question Number 85262 Answers: 1 Comments: 6
$$\mathrm{find}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{symmetry}\:\mathrm{of}\:\mathrm{the}\:\mathrm{curve} \\ $$$$\:\:\:{y}\:=\:\frac{\mathrm{1}}{{x}\:+\:\mathrm{2}} \\ $$
Question Number 85261 Answers: 2 Comments: 1
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{1}+\sqrt{−\mathrm{3}}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} \\ $$$$ \\ $$$$\mathrm{help}\:\mathrm{please} \\ $$
Question Number 85260 Answers: 1 Comments: 1
$$\mathrm{Evaluate}\:\mathrm{using}\:\mathrm{cauchy}'\mathrm{s}\:\mathrm{integral}\: \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{c}} \:\frac{\mathrm{e}^{\mathrm{i}\pi} }{\left(\mathrm{z}^{\mathrm{2}} +\mathrm{4}\right)^{\mathrm{2}} \left(\mathrm{z}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dz} \\ $$$$\mathrm{where}\:\mathrm{c}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{with}\:\mid\mathrm{z}−\mathrm{i}\mid=\mathrm{3}.\mathrm{5} \\ $$$$ \\ $$$$\mathrm{help}\:\mathrm{please} \\ $$
Question Number 85256 Answers: 0 Comments: 3
$$\int\underset{\mathrm{0}} {\overset{\:\mathrm{1}} {\:}}\:\frac{\mathrm{sin}\:\left(\mathrm{ln}\:\mathrm{x}\right)}{\mathrm{ln}\:\left(\mathrm{x}\right)}\:\mathrm{dx}\: \\ $$
Question Number 85254 Answers: 0 Comments: 0
Question Number 85250 Answers: 0 Comments: 0
$$\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{general}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{singular}}\:\boldsymbol{\mathrm{solution}}\:\boldsymbol{\mathrm{of}}\: \\ $$$$\:\left(\mathrm{i}\right).\:\boldsymbol{\mathrm{y}}=\:\boldsymbol{\mathrm{px}}\:+\:\boldsymbol{\mathrm{p}}^{\boldsymbol{\mathrm{n}}} \\ $$$$\left(\mathrm{ii}\right).\:\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{a}}\right)\boldsymbol{\mathrm{p}}^{\mathrm{2}} +\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{y}}\right)\boldsymbol{\mathrm{p}}−\boldsymbol{\mathrm{y}}=\mathrm{0} \\ $$$$\: \\ $$
Question Number 85249 Answers: 0 Comments: 0
Question Number 85248 Answers: 0 Comments: 1
$$\mathrm{find}\:\mathrm{minimum} \\ $$$$\mathrm{y}\:=\:\mathrm{2}\mid\mathrm{x}−\mathrm{3}\mid\:+\:\mid\mathrm{4x}+\mathrm{2}\mid\: \\ $$
Question Number 85241 Answers: 1 Comments: 0
Question Number 85240 Answers: 0 Comments: 0
Question Number 85238 Answers: 1 Comments: 0
$${f}\left({x}\right)\:\:=\:\:{x}^{\mathrm{3}} \:+\:\mathrm{3}{x} \\ $$$${f}\:^{−\mathrm{1}} \left({x}\right)\:\:=\:\:? \\ $$
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