Question Number 167981 by mathlove last updated on 31/Mar/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{4}^{{x}} −\mathrm{2}^{{x}} }{\mathrm{8}^{{x}} −\mathrm{4}^{{x}} }=? \\ $$ Answered by mathlove last updated on 31/Mar/22 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 167980 by mathlove last updated on 31/Mar/22 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{16}{x}+\mathrm{1}}−\mathrm{2}{x}+\mathrm{3}=? \\ $$ Commented by cortano1 last updated on 31/Mar/22 $$=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{2}\left({x}−\frac{\mathrm{16}}{\mathrm{8}}\right)−\mathrm{2}{x}+\mathrm{3} \\ $$$$=\:−\mathrm{4}+\mathrm{3}=−\mathrm{1}…
Question Number 167983 by mathlove last updated on 31/Mar/22 $$\underset{{x}\rightarrow\mathrm{2}^{{x}} } {\mathrm{lim}}\left(\frac{{x}+\mathrm{2}}{\mathrm{2}−{x}}\right)=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 167982 by mathlove last updated on 31/Mar/22 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}+\mathrm{3}{x}}{\:\sqrt{{x}^{\mathrm{2}} +{x}−\mathrm{5}}+{x}}=? \\ $$ Commented by greogoury55 last updated on 31/Mar/22 $$=\:\frac{\mathrm{5}}{\mathrm{2}} \\ $$…
Question Number 167970 by qaz last updated on 30/Mar/22 $$\mathrm{Calculate}:\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{k}^{\mathrm{2}} }{\mathrm{n}^{\mathrm{3}} }\centerdot\sqrt[{\mathrm{k}}]{\mathrm{k}}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 167964 by mnjuly1970 last updated on 30/Mar/22 Commented by greogoury55 last updated on 30/Mar/22 $$\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\left(\frac{\sqrt{{x}}−\sqrt{\mathrm{sin}\:{x}}}{\:\sqrt{{x}}}\right)}{{x}^{\mathrm{4}} } \\ $$$$=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2sin}^{\mathrm{2}} \:\left(\frac{\sqrt{{x}}−\sqrt{\mathrm{sin}\:{x}}}{\mathrm{2}\sqrt{{x}}}\right)}{{x}^{\mathrm{4}} } \\…
Question Number 167943 by mathlove last updated on 30/Mar/22 $$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\frac{{e}^{{x}} −{e}^{\mathrm{3}} }{{x}−\mathrm{3}}=? \\ $$$${wiht}\:{out}\:{H},{pital}\:{ruls} \\ $$ Commented by mkam last updated on 30/Mar/22 $$=\:\boldsymbol{{e}}^{\mathrm{3}}…
Question Number 102296 by bemath last updated on 08/Jul/20 $$\underset{{t}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{{t}}\:\underset{\mathrm{0}} {\overset{{t}} {\int}}\:\mathrm{sin}\:\left(\alpha{x}\right)\:\mathrm{cos}\:\left(\beta{x}\right)\:{dx} \\ $$ Answered by john santu last updated on 08/Jul/20 $${assume}\:\alpha,\beta\:>\:\mathrm{0} \\…
Question Number 167662 by mathlove last updated on 22/Mar/22 $$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\left[\sqrt[{\mathrm{4}}]{{log}\sqrt[{\mathrm{3}}]{\mathrm{2}{log}\sqrt{{x}^{\mathrm{3}} +\mathrm{2}}}}\right]=? \\ $$ Answered by alephzero last updated on 23/Mar/22 $$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\sqrt[{\mathrm{4}}]{\mathrm{ln}\:\sqrt[{\mathrm{3}}]{\mathrm{2ln}\:\sqrt{{x}^{\mathrm{3}} +\mathrm{2}}}}\:= \\…
Question Number 167663 by mathlove last updated on 22/Mar/22 $$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\left[{log}\left(\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{\mathrm{2}{x}}+\frac{\mathrm{1}}{\mathrm{4}{x}}…….\right)\right]=? \\ $$ Commented by mathlove last updated on 22/Mar/22 $$???? \\ $$ Commented by…