Question Number 200105 by cortano12 last updated on 14/Nov/23 Commented by mr W last updated on 14/Nov/23 Commented by mr W last updated on 14/Nov/23…
Question Number 200139 by hardmath last updated on 14/Nov/23 $$\mathrm{If} \\ $$$$\mathrm{x}\::\:\mathrm{y}\::\:\mathrm{z}\:=\:\frac{\mathrm{1}}{\mathrm{7}}\::\:\frac{\mathrm{1}}{\mathrm{3}}\::\:\frac{\mathrm{1}}{\mathrm{21}} \\ $$$$\mathrm{5x}\:−\:\mathrm{2y}\:+\:\mathrm{z}\:=\:\mathrm{16} \\ $$$$ \\ $$$$\mathrm{Find}:\:\:\:\mathrm{y}\:=\:? \\ $$ Answered by ajfour last updated…
Question Number 200133 by sonukgindia last updated on 14/Nov/23 Answered by Frix last updated on 14/Nov/23 $$\mathrm{You}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\ $$$${x}\approx\mathrm{1}.\mathrm{68421311} \\ $$ Terms of Service Privacy…
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Question Number 200103 by cortano12 last updated on 14/Nov/23 $$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}\:\sqrt{\mathrm{x}+\mathrm{1}}−\mathrm{sin}\:\sqrt{\mathrm{x}}\:=? \\ $$ Answered by Frix last updated on 14/Nov/23 $$\mathrm{sin}\:\alpha\:−\mathrm{sin}\:\beta\:=\mathrm{2cos}\:\frac{\alpha+\beta}{\mathrm{2}}\:\mathrm{sin}\:\frac{\alpha−\beta}{\mathrm{2}} \\ $$$$\mathrm{For}\:\mathrm{large}\:{x}:\:\frac{\sqrt{{x}+\mathrm{1}}+\sqrt{{x}}}{\mathrm{2}}\sim\sqrt{{x}}\:\wedge\:\frac{\sqrt{{x}+\mathrm{1}}−\sqrt{{x}}}{\mathrm{2}}\sim\mathrm{0} \\ $$$$\Rightarrow…
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Question Number 200130 by universe last updated on 14/Nov/23 $$\:\:{solve}\:{by}\:{contour}\:{integrstion} \\ $$$$\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{{dx}}{\mathrm{1}+{a}\mathrm{cos}{x}}\: \\ $$ Answered by Mathspace last updated on 14/Nov/23 $${I}=\int_{\mathrm{0}} ^{\mathrm{2}\pi}…
Question Number 200092 by ajfour last updated on 13/Nov/23 Commented by ajfour last updated on 13/Nov/23 $${If}\:{semicircle}\:{has}\:{radius}\:\mathrm{1},\:{find} \\ $$$${radii}\:{of}\:{blue}\:{and}\:{green}\:{circles}. \\ $$$${One}\:{end}\:{of}\:{each}\:{semicircle}\:{is}\:{at} \\ $$$${center}\:{of}\:{other}. \\ $$…
Question Number 200060 by sonukgindia last updated on 13/Nov/23 Answered by cortano12 last updated on 13/Nov/23 $$\:\mathrm{L}=\:\underset{{b}\rightarrow{a}} {\mathrm{lim}}\:\frac{\mathrm{2}{ab}−{a}\sqrt{{ab}}−{ab}}{\left({a}+\sqrt{{ab}}\right)\left({b}−{a}\right)} \\ $$$$\:\:=\:\underset{{b}\rightarrow{a}} {\mathrm{lim}}\:\frac{{ab}−{a}\sqrt{{ab}}}{\left({a}+\sqrt{{ab}}\right)\left({b}−{a}\right)} \\ $$$$\:=\:\underset{{b}\rightarrow{a}} {\mathrm{lim}}\:\frac{\sqrt{{ab}}\:\left(\sqrt{{ab}}−{a}\right)}{\left({a}+\sqrt{{ab}}\right)\left({b}−{a}\right)}\: \\…
Question Number 200061 by universe last updated on 13/Nov/23 $$\:\:\:\:\int_{−\infty} ^{+\infty} \frac{{x}\mathrm{sin}{x}\:}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{4}\right)}{dx}\:\:=\:\:\:?? \\ $$ Answered by witcher3 last updated on 13/Nov/23 $$\int_{−\infty} ^{\infty}…