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Question Number 90030 Answers: 0 Comments: 0
Question Number 90024 Answers: 0 Comments: 2
$$\mathrm{sinh}^{−\mathrm{1}} \left[\mathrm{ln}\left({x}\:+\:\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{1}}\:\right)\right]\:=\:? \\ $$
Question Number 90023 Answers: 1 Comments: 0
$$\:\int\:{e}^{\mid{x}\mid} \:{dx}\:=\:??? \\ $$
Question Number 90019 Answers: 1 Comments: 0
$$\mathrm{find}\:\mathrm{the}\:\mathrm{gcd}\left(\mathrm{2467},\:\mathrm{1367}\right) \\ $$
Question Number 90018 Answers: 1 Comments: 2
$$\mathrm{expand}\:,\:\mathrm{ln}\left(\mathrm{1}\:+\:\mathrm{sin}\:{x}\right)\:\mathrm{right}\:\mathrm{up}\:\mathrm{to}\:\mathrm{the}\:\mathrm{term}\:\mathrm{in}\:{x}^{\mathrm{3}} \\ $$
Question Number 90013 Answers: 1 Comments: 2
$$−{p}^{\mathrm{2}} +\mathrm{2027}=−{q}^{\mathrm{2}} \\ $$$${p}+{q}=? \\ $$
Question Number 90011 Answers: 0 Comments: 6
Question Number 90009 Answers: 0 Comments: 0
$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{2}{n}+\mathrm{1}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }=? \\ $$
Question Number 90003 Answers: 0 Comments: 0
$${show}\:{that} \\ $$$$\int_{−\infty} ^{\infty} \frac{{dx}}{\mathrm{1}+\left({x}+{tan}\left({x}\right)\right)^{\mathrm{2}\:} }=\pi \\ $$
Question Number 89994 Answers: 2 Comments: 0
$$\mathrm{x}−\mathrm{y}=\mathrm{3}\sqrt{\mathrm{xy}} \\ $$$$\left(\frac{\mathrm{x}}{\mathrm{y}}−\mathrm{1}\right)^{\mathrm{3}} +\left(\frac{\mathrm{y}}{\mathrm{x}}−\mathrm{1}\right)^{\mathrm{3}} \:=\:? \\ $$
Question Number 89991 Answers: 0 Comments: 2
$$\mathrm{if}\:\mathrm{a},\mathrm{b}\:>\:\mathrm{0}\:\mathrm{and}\:\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }\:=\:\frac{\mathrm{5}}{\mathrm{3}} \\ $$$$\mathrm{find}\:\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{ab}} \\ $$
Question Number 89986 Answers: 0 Comments: 3
$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(−\mathrm{1}\right)^{\lfloor\frac{\mathrm{1}}{{x}}\rfloor} \:{dx} \\ $$
Question Number 89980 Answers: 0 Comments: 2
Question Number 89978 Answers: 0 Comments: 1
$$\left(\mathrm{x}\:\frac{\mathrm{dy}}{\mathrm{dx}}−\mathrm{y}\right)\left(\mathrm{cos}\:\left(\frac{\mathrm{2y}}{\mathrm{x}}\right)\right)\:=\:−\mathrm{3x}^{\mathrm{4}} \\ $$
Question Number 89977 Answers: 0 Comments: 2
Question Number 89973 Answers: 1 Comments: 1
$${x}\:\frac{{dy}}{{dx}}\:−{y}\:=\:{x}^{\mathrm{2}} \:\mathrm{tan}\:\left(\frac{{y}}{{x}}\right)\: \\ $$
Question Number 89970 Answers: 0 Comments: 1
$$\mathrm{xy}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{y}^{\mathrm{2}} \left(\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\right)\: \\ $$
Question Number 89955 Answers: 1 Comments: 2
$$\mathrm{9}^{\mathrm{x}+\mathrm{1}} \nmid\mathrm{28}\left(\mathrm{3}^{\mathrm{x}} \right)+\mathrm{3}=\mathrm{0} \\ $$
Question Number 89953 Answers: 0 Comments: 1
$$\mathrm{solvethefollowingequation} \\ $$$$\mathrm{5}^{\mathrm{2x}+\mathrm{y}} =\mathrm{625and2}^{\mathrm{4x}\nmid\mathrm{2y}} =\frac{\mathrm{1}}{\mathrm{6}} \\ $$
Question Number 89951 Answers: 0 Comments: 1
$$\mathrm{log}\:_{\mathrm{2}} \:\left(\mathrm{sin}\:\left({x}+\frac{\mathrm{5}\pi}{\mathrm{12}}\right)\right)\:+\:\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{12}}\right)\right)=−\mathrm{1} \\ $$
Question Number 89950 Answers: 0 Comments: 1
Question Number 89946 Answers: 1 Comments: 0
$$\int\underset{−\frac{\pi}{\mathrm{2}}} {\overset{\frac{\pi}{\mathrm{2}}} {\:}}\:\frac{\mathrm{dx}}{\mathrm{1}+\mathrm{e}^{\mathrm{sin}\:\mathrm{x}} } \\ $$
Question Number 89958 Answers: 0 Comments: 1
$${prove}\:{that}\:\left(\mathrm{1}+\mathrm{sin}\:{x}/\mathrm{1}+\mathrm{cos}\:\mathrm{3}\left(\mathrm{1sin}\:{x}/\mathrm{1}+\mathrm{cosec}\:{x}\right)={tanx}\right. \\ $$
Question Number 89956 Answers: 0 Comments: 1
$$\mathrm{simplify}\kappa\mathrm{giving}\kappa\mathrm{your}\kappa\mathrm{answer}\kappa\mathrm{in}\kappa\mathrm{index}\kappa\mathrm{form} \\ $$$$\sqrt{\frac{\mathrm{ac}^{\mathrm{2}} }{\mathrm{9a}^{\mathrm{2}} \mathrm{c}^{\mathrm{4}} }} \\ $$
Question Number 89938 Answers: 0 Comments: 1
$$\mathrm{If}\:\mathrm{x}\left(\mathrm{x}+\mathrm{1}\right)\:=\:\mathrm{1}\: \\ $$$$\mathrm{find}\:\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} −\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$
Question Number 89937 Answers: 0 Comments: 1
$${Prove}\:{that}\:{for}\:{all}\:{complex}\:{such}\:{as}\:\mid{z}\mid<\mathrm{1}= \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{z}^{{n}} }{\left({z}^{{n}} −\mathrm{1}\right)^{\mathrm{2}} }\:+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{nz}^{{n}} }{{z}^{{n}} −\mathrm{1}}\:=\:\mathrm{0}\: \\ $$
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