Question Number 174276 by cortano1 last updated on 28/Jul/22 Answered by blackmamba last updated on 28/Jul/22 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt[{\mathrm{2022}}]{\mathrm{cos}\:\left(\mathrm{2021}{x}\right)}}{{x}^{\mathrm{2}} }\:= \\ $$$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt[{\mathrm{2022}}]{\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \left(\frac{\mathrm{2021}{x}}{\mathrm{2}}\right)}}{{x}^{\mathrm{2}} } \\…
Question Number 174258 by blackmamba last updated on 28/Jul/22 $$\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\sqrt{{x}^{\mathrm{4}} −{x}^{\mathrm{3}} }}\:−\:{x}\:=? \\ $$ Answered by cortano1 last updated on 28/Jul/22 $$\:\:=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{{x}^{\mathrm{4}} −{x}^{\mathrm{3}}…
Question Number 108623 by bemath last updated on 18/Aug/20 $$\:\:\frac{\supset\mathcal{B}{e}\mathcal{M}{ath}\supset}{\bigstar} \\ $$$$\:\left(\mathrm{1}\right)\underset{{b}\rightarrow{a}} {\mathrm{lim}}\:\frac{{b}\sqrt{{a}}−{a}\sqrt{{b}}}{{a}\sqrt{{a}}+{b}\sqrt{{a}}−\mathrm{2}{a}\sqrt{{a}}} \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3}{e}^{\mathrm{2}{x}} +{e}^{{x}} −\mathrm{4}}{{x}} \\ $$ Answered by ajfour last updated…
Question Number 174152 by cortano1 last updated on 26/Jul/22 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}\mathrm{cos}\:{x}+\mathrm{2}{x}\right)}{\mathrm{5}{x}^{\mathrm{2}} }\:=? \\ $$ Answered by CElcedricjunior last updated on 26/Jul/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−{sin}\left(\frac{\boldsymbol{\pi}}{\mathrm{2}}{cosx}+\mathrm{2}{x}\right)}{\mathrm{5}\boldsymbol{{x}}^{\mathrm{2}} }=\frac{\mathrm{0}}{\mathrm{0}}=\boldsymbol{{F}\mathrm{I}} \\…
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Question Number 174071 by alcohol last updated on 24/Jul/22 Answered by aleks041103 last updated on 24/Jul/22 $$ . \\ $$$$\mathrm{1}. \\ $$$${F}\left({x}\right)=\int_{\mathrm{0}} ^{\:{x}} \frac{{dt}}{\:\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}=\int_{\mathrm{0}}…
Question Number 174056 by cortano1 last updated on 23/Jul/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 108469 by bemath last updated on 17/Aug/20 $$\:\:\:\frac{\subset\mathcal{B}{e}\mathcal{M}{ath}\supset}{\cap} \\ $$$$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:{x}\:\sqrt{\mathrm{cos}\:\mathrm{2}{x}}\:\sqrt{\mathrm{cos}\:\mathrm{3}{x}}…\sqrt{\mathrm{cos}\:{nx}}}{{x}^{\mathrm{2}} }\:? \\ $$$$\left(\mathrm{2}\right){x}^{\mathrm{2}} {y}''+{xy}'−\mathrm{4}{y}=\mathrm{0};\:{y}\left(\mathrm{1}\right)=\mathrm{2}\:{and} \\ $$$$\:\:\:{y}'\left(\mathrm{1}\right)=\mathrm{0} \\ $$$$\left(\mathrm{3}\right){find}\:{the}\:{probability}\:{that}\:{a}\:{person}\:\:{throwing}\:{three} \\ $$$${coins}\:{at}\:{once}\:{will}\:{get}\:{all}\:{the}\:{face}\:{or}\: \\ $$$${everything}\:{back}\:{for}\:{second}\:{time}\:{at}…
Question Number 42933 by Joel578 last updated on 05/Sep/18 $$\mathrm{Suppose}\:\mathrm{that}\:{f}\:\mathrm{and}\:{g}\:\mathrm{are}\:\mathrm{two}\:\mathrm{functions}\:\mathrm{such}\:\mathrm{that} \\ $$$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:{g}\left({x}\right)\:=\:\mathrm{0}\:\:\:\:\mathrm{and}\:\:\:\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:\frac{{f}\left({x}\right)}{{g}\left({x}\right)}\:\:\:\mathrm{exist}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:{f}\left({x}\right)\:=\:\mathrm{0} \\ $$ Commented by MrW3 last updated on…
Question Number 42897 by Joel578 last updated on 04/Sep/18 Commented by Joel578 last updated on 04/Sep/18 $$\mathrm{For}\:\mathrm{question}\:\left({c}\right), \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{G}\left({x}\right)\:=\:\mathrm{2}\:\:\:\mathrm{or}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{G}\left({x}\right)\:=\:\mathrm{0}\:? \\ $$ Answered by…