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Category: Limits

Can-someone-please-explain-why-lim-x-x-x-2-

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} \\…

lim-n-S-i-1-n-i-n-1-L-S-R-S-gt-0-What-can-we-tell-about-L-Does-there-exist-a-limit-Is-it-positive-negative-

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}?…

lim-x-2a-x-2a-x-2a-x-2-4a-2-where-a-gt-0-

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}\: \\…

1-2-3-4-S-2-4-6-8-10-2S-S-2S-1-3-5-7-2S-S-lim-x-n-n-1-2-lim-x-n-2-S-1-2-3-4-

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…

solve-L-lim-x-0-e-x-1-1-x-x-2-

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}}…