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Category: Limits

lim-x-pi-2-cos-x-sin-x-cos-x-1-3-sin-x-

Question Number 161319 by cortano last updated on 16/Dec/21 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:{x}}{\:\sqrt[{\mathrm{3}}]{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}−\mathrm{sin}\:{x}}=? \\ $$ Answered by som(math1967) last updated on 16/Dec/21 $$\underset{\boldsymbol{{x}}\rightarrow\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\boldsymbol{{lim}}}\:\frac{\boldsymbol{{cosx}}\left\{\left(\boldsymbol{{sinx}}+\boldsymbol{{cosx}}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} +\left(\boldsymbol{{sinx}}+\boldsymbol{{cosx}}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \boldsymbol{{sinx}}+\boldsymbol{{sin}}^{\mathrm{2}} \boldsymbol{{x}}\right\}}{\boldsymbol{{sinx}}+\boldsymbol{{cosx}}−\boldsymbol{{sin}}^{\mathrm{3}}…

lim-n-k-1-n-k-n-n-

Question Number 161202 by qaz last updated on 14/Dec/21 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\left(\frac{\mathrm{k}}{\mathrm{n}}\right)^{\mathrm{n}} =? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-161186

Question Number 161186 by mathlove last updated on 13/Dec/21 Answered by Rasheed.Sindhi last updated on 13/Dec/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\sqrt{\mathrm{2}}\:{x}+\mathrm{10}}{\:\sqrt{\mathrm{2}}\:{x}−\mathrm{11}}\right)^{\frac{\mathrm{2}{x}−\mathrm{1}}{{x}+\mathrm{1}}} \\ $$$$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\cancel{{x}}\left(\sqrt{\mathrm{2}}\:+\frac{\mathrm{10}}{{x}}\right)}{\:\cancel{{x}}\left(\sqrt{\mathrm{2}}\:−\frac{\mathrm{11}}{{x}}\right)}\right)^{\frac{\cancel{{x}}\left(\mathrm{2}−\frac{\mathrm{1}}{{x}}\right)}{\cancel{{x}}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)}} \\ $$$$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\sqrt{\mathrm{2}}\:+\frac{\mathrm{10}}{{x}}}{\:\sqrt{\mathrm{2}}\:−\frac{\mathrm{11}}{{x}}}\right)^{\frac{\mathrm{2}−\frac{\mathrm{1}}{{x}}}{\mathrm{1}+\frac{\mathrm{1}}{{x}}}} \\…