Question Number 170812 by MathsFan last updated on 31/May/22 $$\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\frac{\boldsymbol{\mathrm{x}}+\mathrm{1}}{\:\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{9}}} \\ $$$$\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{horizontal}}\:\boldsymbol{\mathrm{asymptote}} \\ $$ Answered by Mathspace last updated on 31/May/22 $${lim}_{{x}\rightarrow−\infty} {f}\left({x}\right)={lim}_{{x}\rightarrow−\infty} \frac{{x}+\mathrm{1}}{\mid{x}\mid\sqrt{\mathrm{1}+\frac{\mathrm{9}}{{x}^{\mathrm{2}}…
Question Number 170811 by mokys last updated on 31/May/22 $${find}\:{minimum}\:{and}\:{maximum}\:{z}\:=\:{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}{y}^{\mathrm{2}} +\mathrm{2}\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 170809 by thean last updated on 31/May/22 Answered by som(math1967) last updated on 31/May/22 $$\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{e}^{−\mathrm{1}} \left({e}^{\mathrm{2}{x}} −\mathrm{1}\right){sin}\mathrm{3}{x}}{{x}^{\mathrm{2}} } \\ $$$$=\frac{\mathrm{6}}{{e}}\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{\left({e}^{\mathrm{2}{x}} −\mathrm{1}\right)}{\mathrm{2}{x}}×\frac{{sin}\mathrm{3}{x}}{\mathrm{3}{x}}…
Question Number 170810 by MathsFan last updated on 31/May/22 $$ \\ $$The mean height of a population of girls aged 15 to 19 years in…
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Question Number 105266 by mohammad17 last updated on 27/Jul/20 Answered by mathmax by abdo last updated on 27/Jul/20 $$\mathrm{we}\:\mathrm{have}\:\mathrm{L}\left(\mathrm{t}^{\frac{\mathrm{3}}{\mathrm{2}}} \right)\:=\int_{\mathrm{0}} ^{\infty} \:\mathrm{x}^{\frac{\mathrm{3}}{\mathrm{2}}} \:\mathrm{e}^{−\mathrm{tx}} \mathrm{dx}\:=_{\mathrm{tx}\:=\mathrm{u}} \:\:\int_{\mathrm{0}}…
Question Number 170800 by thfchristopher last updated on 31/May/22 $$\mathrm{Prove}\:\mathrm{that},\:\mathrm{for}\:\mathrm{any}\:\mathrm{real}\:\mathrm{number}\:{x}\:\mathrm{and}\:\mathrm{odd}\:\mathrm{positive}\:\mathrm{integer}\:{n}, \\ $$$$\:\:\:\:\:\:\:\mathrm{cos}^{{n}} {x}=\frac{\mathrm{1}}{\mathrm{2}^{{n}+\mathrm{1}} }\underset{{k}=\mathrm{0}} {\overset{\left({n}−\mathrm{1}\right)/\mathrm{2}} {\sum}}{C}_{{k}} ^{{n}} \mathrm{cos}\:\left({n}−\mathrm{2}{k}\right){x} \\ $$ Answered by aleks041103 last updated…
Question Number 170796 by Beginner last updated on 31/May/22 Answered by som(math1967) last updated on 31/May/22 $$\left[\frac{\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{3}}} \left\{\left(\sqrt{\mathrm{3}}\right)^{\sqrt{\mathrm{2}}} +\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{3}}} \right\}}{\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{2}}} \left\{\left(\sqrt{\mathrm{3}}\right)^{\sqrt{\mathrm{2}}} +\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{3}}} \right\}}\right]^{\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}}} \\ $$$$\left(\sqrt{\mathrm{2}}\right)^{\frac{\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}}}…