Question Number 30553 by abdo imad last updated on 23/Feb/18 $${find}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \left(\mathrm{1}+{sinx}\right)^{{x}} \:−\left(\mathrm{1}+{x}\right)^{{sinx}} . \\ $$ Commented by Cheyboy last updated on 23/Feb/18 $${by}\:{direct}\:{subtitution} \\…
Question Number 96078 by john santu last updated on 29/May/20 $$\underset{\left({x},\mathrm{y}\right)\rightarrow\left(\mathrm{1},\mathrm{2}\right)} {\mathrm{lim}}\:\mathrm{sin}\:\left(\frac{\mathrm{x}−\mathrm{1}}{\mathrm{y}−\mathrm{2}}\right)\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 161612 by cortano last updated on 20/Dec/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\sqrt[{{x}}]{\mathrm{cos}\:\sqrt{{x}}}\:=? \\ $$ Answered by Ar Brandon last updated on 20/Dec/21 $${A}=\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\sqrt[{{x}}]{\mathrm{cos}\sqrt{{x}}}=\underset{{x}\rightarrow\mathrm{0}^{+}…
Question Number 30524 by abdo imad last updated on 22/Feb/18 $${let}\:{w}_{{n}} =\:\sum_{{k}=\mathrm{2}} ^{{n}} \:\:\:\:\frac{\mathrm{1}}{{k}^{\mathrm{2}} −\mathrm{1}}\:\:{find}\:{lim}_{{n}\rightarrow\infty} \:{w}_{{n}} \:. \\ $$ Commented by abdo imad last updated…
Question Number 161586 by blackmamba last updated on 20/Dec/21 $$\:\:\underset{{x}\rightarrow\mathrm{2}^{−} } {\mathrm{lim}}\:\frac{\mathrm{2}−\mathrm{2cos}\:\sqrt{{x}−\mathrm{2}}}{\left({x}−\mathrm{2}\right)^{\mathrm{2}} }\:=? \\ $$ Commented by cortano last updated on 20/Dec/21 Commented by mathmax…
Question Number 30514 by abdo imad last updated on 22/Feb/18 $${find}\:{lim}_{{n}\rightarrow\infty} \:\prod_{{k}=\mathrm{1}} ^{{n}} \:\left(\mathrm{1}−\:\frac{{k}^{\mathrm{2}} }{{n}^{\mathrm{3}} }\right).\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30511 by abdo imad last updated on 22/Feb/18 $${find}\:\:{lim}_{{x}\rightarrow+\infty} \:\:{e}^{{x}} \:\left[\frac{\mathrm{1}}{{x}}\right]. \\ $$ Commented by abdo imad last updated on 24/Feb/18 $${for}\:{x}>\mathrm{1}\:\Rightarrow\:\mathrm{0}<\frac{\mathrm{1}}{{x}}<\mathrm{1}\:\Rightarrow\:\left[\frac{\mathrm{1}}{{x}}\right]=\mathrm{0}\:\Rightarrow\:\forall{x}>\mathrm{1}\:{e}^{{x}} \:\left[\frac{\mathrm{1}}{{x}}\right]=\mathrm{0}\Rightarrow…
Question Number 161583 by cortano last updated on 19/Dec/21 $$\:\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{sin}\:\frac{\pi}{{x}}}{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{4}}\:=? \\ $$$$\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{3}} −\mathrm{8}+\mathrm{sin}\:\pi{x}}{\mathrm{2}−{x}}=? \\ $$$$\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\mathrm{cos}\:\left(\frac{\pi}{{x}+\mathrm{1}}\right)}=? \\ $$ Commented by blackmamba…
Question Number 30510 by abdo imad last updated on 22/Feb/18 $${find}\:\:{lim}_{{x}\rightarrow\mathrm{0}^{+\:} } \:\:\:\:\sqrt{{x}}\:\left[\:\frac{\mathrm{1}}{{x}}\right]\:\:{and}\:{lim}_{{x}\rightarrow+\infty} \:\:\frac{\left[{x}\right]}{{x}}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30504 by abdo imad last updated on 22/Feb/18 $${find}\:{lim}_{{x}\rightarrow\infty} \:{x}^{\mathrm{2}} \left(\:{e}^{\frac{\mathrm{1}}{{x}}} \:\:\:−\:{e}^{\frac{\mathrm{1}}{{x}+\mathrm{1}}} \right)\:. \\ $$ Answered by sma3l2996 last updated on 24/Feb/18 $$…