Question Number 111923 by bemath last updated on 05/Sep/20 $$\sqrt{{bemath}\:} \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}\:}]{\mathrm{cos}\:\mathrm{4}{x}}\:−\mathrm{1}}{\mathrm{cos}\:\mathrm{3}{x}−\mathrm{cos}\:\mathrm{9}{x}}\:? \\ $$ Answered by bobhans last updated on 05/Sep/20 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}\:}]{\mathrm{cos}\:\mathrm{4x}}\:−\mathrm{1}}{\mathrm{cos}\:\mathrm{3x}\:−\:\mathrm{cos}\:\mathrm{9x}}\:? \\…
Question Number 111914 by bemath last updated on 05/Sep/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{8}{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{4}+\mathrm{sin}\:\mathrm{6}{x}}\:−\sqrt{\mathrm{tan}\:\mathrm{6}{x}+\mathrm{4}}}\:? \\ $$ Answered by bobhans last updated on 05/Sep/20 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{8x}^{\mathrm{3}} }{\:\sqrt{\mathrm{4}+\mathrm{sin}\:\mathrm{6x}}\:−\sqrt{\mathrm{4}+\mathrm{tan}\:\mathrm{6x}}}\:=\: \\…
Question Number 111907 by bemath last updated on 05/Sep/20 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{20}}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{tan}\:\mathrm{5}{x}}{\mathrm{sin}\:\mathrm{5}{x}−\mathrm{cos}\:\mathrm{5}{x}}\:? \\ $$ Answered by john santu last updated on 05/Sep/20 Answered by john santu…
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Question Number 111882 by bemath last updated on 05/Sep/20 $$\:\:\sqrt{{bemath}} \\ $$$$\left(\mathrm{1}\right)\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left[\frac{{x}^{\mathrm{2}} }{{x}+\mathrm{1}}\:−\:\frac{{x}^{\mathrm{2}} }{{x}+\mathrm{3}}\:\right]\:? \\ $$$$\left(\mathrm{2}\right)\:{prove}\:{that}\:{n}^{\mathrm{2}} \:\leqslant\:\mathrm{2}^{{n}} \:{for}\:\forall{n}\in\mathbb{N} \\ $$$${by}\:{mathematical}\:{induction} \\ $$ Answered by…
Question Number 46330 by Saorey last updated on 24/Oct/18 $$\mathrm{pls}\:\mathrm{help}\:\mathrm{me}! \\ $$$$\mathrm{L}=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\sqrt[{\mathrm{13}}]{\mathrm{x}}−\sqrt[{\mathrm{7}}]{\mathrm{x}}}{\:\sqrt[{\mathrm{5}}]{\mathrm{x}}−\sqrt[{\mathrm{3}}]{\mathrm{x}}} \\ $$ Commented by MJS last updated on 24/Oct/18 $$\mathrm{I}\:\mathrm{would}\:\mathrm{again}\:\mathrm{recommend}\:\mathrm{l}'\mathrm{Hopital} \\ $$$$\underset{{x}\rightarrow\mathrm{1}}…
Question Number 46187 by annika0209 last updated on 22/Oct/18 $$\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{n}×\mathrm{n}^{\frac{\mathrm{1}}{\mathrm{n}}} }=?\:\:\:\:\:\:\:\:\mathrm{please}\:\mathrm{help}\:\mathrm{me}!!!! \\ $$$$ \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 46146 by Sanjarbek last updated on 21/Oct/18 Commented by Meritguide1234 last updated on 21/Oct/18 $${e}^{\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right){dx}} \\ $$ Commented by Meritguide1234…
Question Number 46136 by Meritguide1234 last updated on 21/Oct/18 Answered by ajfour last updated on 21/Oct/18 $$\left(\mathrm{cos}\:{nx}\right)^{\mathrm{1}/{n}} \:=\:\left(\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \:\frac{{nx}}{\mathrm{2}}\right)^{\mathrm{1}/{n}} \\ $$$$\:\:\:\:\:{if}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:{then}\:\:=\:\mathrm{1}−\frac{\mathrm{2}}{{n}}\left(\frac{{n}^{\mathrm{2}} {x}^{\mathrm{2}} }{\mathrm{4}}\right) \\…
Question Number 46040 by annika0209 last updated on 20/Oct/18 Terms of Service Privacy Policy Contact: info@tinkutara.com