Question Number 212097 by liuxinnan last updated on 30/Sep/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left({x}^{\mathrm{2}} +{e}^{{x}} \right)^{\frac{\mathrm{1}}{{x}}} =? \\ $$ Answered by mehdee7396 last updated on 30/Sep/24 $${lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{x}^{\mathrm{2}}…
Question Number 211759 by liuxinnan last updated on 20/Sep/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\mathrm{sin}\:{x}} −{e}^{{x}} }{\mathrm{sin}\:{x}−{x}}=? \\ $$ Commented by liuxinnan last updated on 20/Sep/24 Answered by TonyCWX08…
Question Number 211745 by Majak last updated on 19/Sep/24 $$\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\left(\mathrm{10}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{20}\right) \\ $$ Commented by Majak last updated on 19/Sep/24 $${need}\:{help}\:{guy} \\ $$ Answered…
Question Number 211717 by liuxinnan last updated on 18/Sep/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{li}{m}}\frac{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} −\mathrm{1}}{{e}^{{x}^{\mathrm{2}} } −\mathrm{1}}=? \\ $$ Answered by BHOOPENDRA last updated on 18/Sep/24 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 211716 by liuxinnan last updated on 18/Sep/24 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}×\mathrm{3}}+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}×\mathrm{3}×\centerdot\centerdot\centerdot×{x}}\right)=? \\ $$ Answered by BHOOPENDRA last updated on 18/Sep/24 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\underset{{n}=\mathrm{0}\:} {\overset{{x}} {\sum}}\frac{\mathrm{1}}{{n}!}−\mathrm{1}\right) \\…
Question Number 211295 by efronzo1 last updated on 05/Sep/24 $$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left.\mathrm{x}−\underset{\mathrm{n}\:\mathrm{times}} {\underbrace{\mathrm{sin}\:\left(\mathrm{sin}\:\left(\mathrm{sin}\:\left(….\left(\mathrm{sin}\:\mathrm{x}\right)\right)\right)\right)\right)}}}{\mathrm{x}^{\mathrm{3}} } \\ $$ Answered by mahdipoor last updated on 05/Sep/24 $$ \\ $$$${get}\:{f}_{{n}}…
Question Number 211241 by efronzo1 last updated on 01/Sep/24 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{x}^{\mathrm{2}} −\mathrm{cos}\:\left(\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\:\right)}{\mathrm{x}^{\mathrm{6}} }\:=? \\ $$ Commented by Frix last updated on 01/Sep/24 $$\mathrm{Using}\:\mathrm{Taylor}\:\mathrm{polynomials}\:\mathrm{I}\:\mathrm{get}\:−\frac{\mathrm{1}}{\mathrm{3}} \\…
Question Number 210918 by VICHET last updated on 22/Aug/24 Answered by Frix last updated on 22/Aug/24 $$\mathrm{Let}\:{x}={t}+\mathrm{11} \\ $$$$\underset{{t}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\frac{\mid{x}\mid}{{x}}\:=\underset{{t}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\frac{−{x}}{{x}}\:=−\mathrm{1} \\ $$$$\underset{{t}\rightarrow\mathrm{0}^{+}…
Question Number 210769 by zhou0429 last updated on 19/Aug/24 Commented by Frix last updated on 19/Aug/24 $$\int\frac{{dx}}{{x}^{{n}} +\mathrm{1}}={x}×_{\mathrm{2}} {F}_{\mathrm{1}} \:\left(\mathrm{1},\:\frac{\mathrm{1}}{{n}};\:\frac{{n}+\mathrm{1}}{{n}};\:−{x}^{{n}} \right)\:+{C} \\ $$ Terms of…
Question Number 210674 by noraell last updated on 15/Aug/24 Answered by BHOOPENDRA last updated on 16/Aug/24 $${f}\left({x}\right)=\frac{{x}^{\mathrm{2}} }{{k}^{\mathrm{2}} \:\left\{−\mathrm{1}+\sqrt{\left.−\mathrm{4}{x}^{\mathrm{4}} −\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}\right\}}\:\right.} \\ $$$$\left\{{lim}\:{x}\rightarrow\mathrm{0}\:\frac{{sinx}}{{x}}=\mathrm{1},{limx}\rightarrow\mathrm{0}\:\frac{{tanx}}{{x}}=\mathrm{1}\right\} \\ $$$${conjugate}\:{multiplication}…