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]=? \\ $$ Commented by mathlove last updated on 22/Mar/22 $$???? \\ $$ Commented by…
Question Number 36563 by bshahid010@gmail.com last updated on 03/Jun/18 Commented by prof Abdo imad last updated on 03/Jun/18 $${let}\:{use}\:{the}\:{changement}\:\:\frac{{a}}{{x}}\:={t} \\ $$$${lim}_{{x}\rightarrow{a}} \left(\mathrm{2}−\frac{{a}}{{x}}\right)^{{tan}\left(\frac{\pi{x}}{\mathrm{2}{a}}\right)} \:={lim}_{{t}\rightarrow\mathrm{1}} \left(\mathrm{2}−{t}\right)^{{tan}\left(\:\frac{\pi}{\mathrm{2}{t}}\right)} \\…
Question Number 167624 by mnjuly1970 last updated on 21/Mar/22 $$ \\ $$$$\:\:{solve} \\ $$$$\:\:\Omega\:={lim}_{\:{n}\rightarrow\infty} {n}^{\:\mathrm{2}} .\:{ln}\left(\:{n}\:.\:{sin}\left(\frac{\mathrm{1}}{{n}}\right)\right)=? \\ $$$$ \\ $$ Answered by qaz last updated…
Question Number 167617 by mathlove last updated on 21/Mar/22 $$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left[{tan}\left(\frac{\pi}{\mathrm{4}}−{x}\right)\right]^{{cotx}} =? \\ $$$$\left(\mathrm{2}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left[\frac{\mathrm{1}}{\mathrm{sin}\:{x}}−\frac{\mathrm{1}}{{x}}\right]=? \\ $$ Answered by cortano1 last updated on 21/Mar/22 $$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 167615 by cortano1 last updated on 20/Mar/22 $$\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{3}+\mathrm{x}}\:\sqrt[{\mathrm{3}}]{\mathrm{7}+\mathrm{x}^{\mathrm{3}} }−\mathrm{4}}{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} }\:=? \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 167593 by cortano1 last updated on 20/Mar/22 Answered by qaz last updated on 20/Mar/22 $$\mathrm{A}=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{17}−\mathrm{2}\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} }\centerdot\sqrt[{\mathrm{3}}]{\mathrm{3}\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{3}} +\mathrm{3}}−\mathrm{9}}{\mathrm{x}^{\mathrm{2}} } \\ $$$$=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{9}−\mathrm{2x}^{\mathrm{2}} −\mathrm{8x}}\centerdot\sqrt[{\mathrm{3}}]{\mathrm{3x}^{\mathrm{3}}…