Question Number 80220 by TawaTawa last updated on 01/Feb/20 Commented by kaivan.ahmadi last updated on 01/Feb/20 $$\forall\epsilon>\mathrm{0}\exists\delta>\mathrm{0}\:{s}.{t}\:\mid{x}−\mathrm{3}\mid<\delta\Rightarrow\mid{x}^{\mathrm{2}} −\mathrm{9}\mid<\epsilon \\ $$$$\mid{x}^{\mathrm{2}} −\mathrm{9}\mid=\mid{x}−\mathrm{3}\mid\mid{x}+\mathrm{3}\mid<\epsilon \\ $$$${if}\:\delta=\mathrm{1}\Rightarrow\mid{x}−\mathrm{3}\mid<\mathrm{1}\Rightarrow−\mathrm{1}<{x}−\mathrm{3}<\mathrm{1}\Rightarrow\mathrm{2}<{x}<\mathrm{4}\Rightarrow \\ $$$$\mathrm{5}<{x}+\mathrm{3}<\mathrm{7}\Rightarrow\mid{x}+\mathrm{3}\mid<\mathrm{7}…
Question Number 14593 by 1kanika# last updated on 02/Jun/17 Answered by Tinkutara last updated on 02/Jun/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 80064 by Rio Michael last updated on 30/Jan/20 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\left[\sqrt{\mathrm{1}−{xe}^{{x}} \:}\right] \\ $$ Commented by mathmax by abdo last updated on 30/Jan/20 $${no}\:{its}\:{a}\:{indeterminedform}\:\:{its}\:{not}\:{correct}…
Question Number 80000 by malwaan last updated on 30/Jan/20 $$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{lim}}}\:\frac{\boldsymbol{{arcsin}}\frac{\boldsymbol{{x}}}{\:\sqrt{\mathrm{1}−\boldsymbol{{x}}^{\mathrm{2}} }}}{\boldsymbol{{ln}}\left(\mathrm{1}−\boldsymbol{{x}}\right)}\:=\:−\mathrm{1} \\ $$ Commented by jagoll last updated on 30/Jan/20 $$\mathrm{sin}\:{y}\:=\:\frac{{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:\Rightarrow\frac{{x}^{\mathrm{2}}…
Question Number 79992 by john santu last updated on 29/Jan/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{\mathrm{1}}{\mathrm{x}}\right]\:=\:? \\ $$ Commented by jagoll last updated on 30/Jan/20 $$\mathrm{do}\:\mathrm{not}\:\mathrm{exis}\: \\ $$ Commented…
Question Number 145423 by olalekan2 last updated on 04/Jul/21 Answered by Olaf_Thorendsen last updated on 04/Jul/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+{x}}+\left(\mathrm{1}+{x}\right)^{\mathrm{7}} −\mathrm{2}}{{x}} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}{x}+\mathrm{1}+\mathrm{7}{x}−\mathrm{2}}{{x}} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{1}}{\mathrm{2}}{x}+\mathrm{7}{x}}{{x}}…
Question Number 14336 by tawa tawa last updated on 30/May/17 Commented by ajfour last updated on 30/May/17 $$\mathrm{cos}\:{x}=\mathrm{1}−\left(\mathrm{1}−\mathrm{cos}\:{x}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:=\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right)=\mathrm{1}−{t} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{cos}\:{x}\right)=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left[\left(\mathrm{1}−{t}\right)^{−\mathrm{1}/{t}}…
Question Number 145363 by imjagoll last updated on 04/Jul/21 $$\:\mathrm{Without}\:\mathrm{L}'\mathrm{Hopital}\:\mathrm{rule} \\ $$$$\:\underset{{x}\rightarrow\pi/\mathrm{4}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2}}\:\mathrm{cos}\:\mathrm{x}−\mathrm{1}}{\mathrm{cot}\:\mathrm{x}−\mathrm{1}}\:=? \\ $$ Answered by liberty last updated on 04/Jul/21 $$\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2}}\mathrm{cos}\:{x}−\mathrm{1}}{\mathrm{cot}\:{x}−\mathrm{1}}\: \\…
Question Number 145205 by imjagoll last updated on 03/Jul/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{2}\left(\mathrm{sin}\:\left(\mathrm{sin}\:\mathrm{x}\right)\right)}{\mathrm{x}^{\mathrm{2}} }=? \\ $$ Answered by EDWIN88 last updated on 03/Jul/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{2}\left(\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)\right)}{{x}^{\mathrm{2}} }\: \\…
Question Number 79652 by john santu last updated on 27/Jan/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left[\left(\mathrm{4n}^{\mathrm{2}} −\mathrm{1}\right)\mathrm{ln}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4n}^{\mathrm{2}} }\right)+\mathrm{1}\right]\: \\ $$ Terms of Service Privacy Policy Contact:…