Question Number 70865 by OmerAlattas last updated on 08/Oct/19 Commented by mathmax by abdo last updated on 08/Oct/19 $$=\frac{\mathrm{0}}{\infty}=\mathrm{0} \\ $$ Commented by kaivan.ahmadi last…
Question Number 5286 by FilupSmith last updated on 05/May/16 $$\mathrm{Can}\:\mathrm{someone}\:\mathrm{please}\:\mathrm{explain}\:\mathrm{why}: \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left({x}−{x}^{\mathrm{2}} \right)\:=\:−\infty \\ $$ Commented by FilupSmith last updated on 05/May/16 $$\mathrm{i}\:\mathrm{normally}\:\mathrm{undwrstand}\:\mathrm{limits}\:\mathrm{but} \\…
Question Number 5207 by FilupSmith last updated on 30/Apr/16 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{{S}−\left(\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{i}!\right)}{{n}}−\mathrm{1}={L} \\ $$$${S}\in\mathbb{R},\:\:{S}>\mathrm{0} \\ $$$$ \\ $$$$\mathrm{What}\:\mathrm{can}\:\mathrm{we}\:\mathrm{tell}\:\mathrm{about}\:{L}? \\ $$$$ \\ $$$$\mathrm{Does}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{a}\:\mathrm{limit}? \\ $$$$\mathrm{Is}\:\mathrm{it}\:\mathrm{positive}/\mathrm{negative}?…
Question Number 136278 by adhigenz last updated on 20/Mar/21 $$\mathrm{How}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}? \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\underset{\mathrm{1}} {\overset{{x}} {\int}}\left[\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}}\:−\:{x}\right]\:{dx}}{{x}^{\mathrm{2}} }\:=\:… \\ $$ Answered by MJS_new last updated on…
Question Number 136258 by EDWIN88 last updated on 20/Mar/21 $$\underset{{x}\rightarrow\mathrm{2a}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}−\mathrm{2a}}\:+\:\sqrt{\mathrm{x}}\:−\sqrt{\mathrm{2a}}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{4a}^{\mathrm{2}} }}\:=?\:\mathrm{where}\:\mathrm{a}>\mathrm{0} \\ $$ Answered by liberty last updated on 20/Mar/21 $$\:{L}'{H}\ddot {{o}pital}\: \\…
Question Number 5157 by 1771727373 last updated on 24/Apr/16 $$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+……..={S} \\ $$$$\mathrm{2}+\mathrm{4}+\mathrm{6}+\mathrm{8}+\mathrm{10}+……..=\mathrm{2}{S} \\ $$$${S}\supset\mathrm{2}{S} \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{5}+\mathrm{7}+…………+\left(\mathrm{2}{S}\right)={S} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left\{\frac{{n}\left({n}−\mathrm{1}\right)}{\mathrm{2}}\right\}=+\infty \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left\{{n}^{\mathrm{2}} \right\}=+\infty \\ $$$$\left(+\infty\right)+\left(+\infty\right)={S}=\infty…
Question Number 136093 by mnjuly1970 last updated on 18/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:…..{nice}\:\:\:\:{calculus}….. \\ $$$$\:\:\:\:\:{calculate}\::: \\ $$$$\:\:\:\:\:{lim}_{{n}\rightarrow\infty} \frac{\mathrm{1}}{\:\sqrt{{n}}}\:\underset{{k}=\mathrm{1}\:} {\overset{{n}} {\sum}}{cos}^{\mathrm{2}{n}} \left(\frac{{k}\pi}{{n}}\right)=?? \\ $$$$ \\ $$ Terms of Service…
Question Number 4964 by ankit chakravarti last updated on 27/Mar/16 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{\left(\mathrm{1}−\mathrm{cos}\:\mathrm{2}{x}\right)\centerdot\left(\mathrm{3}+\mathrm{cos}\:{x}\right)}{{x}\centerdot\mathrm{tan4}{x}}=? \\ $$$$ \\ $$ Answered by FilupSmith last updated on 29/Mar/16 Commented by…
Question Number 136026 by mathmax by abdo last updated on 18/Mar/21 $$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{sin}\left(\mathrm{1}−\mathrm{cosx}\right)−\mathrm{xcos}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}\right)}{\mathrm{x}^{\mathrm{3}} } \\ $$ Commented by yutytfjh67ihd last updated on 25/Mar/21 Terms…
Question Number 70364 by 20190927 last updated on 03/Oct/19 $$\mathrm{solve}\:\mathrm{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{e}^{\mathrm{x}} −\frac{\mathrm{1}}{\mathrm{1}−\mathrm{x}}}{\mathrm{x}^{\mathrm{2}} } \\ $$ Commented by kaivan.ahmadi last updated on 03/Oct/19 $${lim}_{{x}\rightarrow\mathrm{0}} \frac{\left(\mathrm{1}−{x}\right){e}^{{x}} −\mathrm{1}}{{x}^{\mathrm{2}}…