Question Number 71317 by aliesam last updated on 13/Oct/19 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{\mid\mathrm{2}{x}−\mathrm{2}\mid−\mid\mathrm{2}{x}+\mathrm{2}\mid}{{x}} \\ $$ Commented by mathmax by abdo last updated on 13/Oct/19 $$={lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{\sqrt{\left(\mathrm{2}{x}−\mathrm{2}\right)^{\mathrm{2}} }−\sqrt{\left(\mathrm{2}{x}+\mathrm{2}\right)^{\mathrm{2}}…
Question Number 5772 by sagarvijay444@gmail.com last updated on 27/May/16 $${q}+\: \\ $$ Commented by FilupSmith last updated on 27/May/16 $$\exists{x}\in\mathbb{Z}^{+} :{x}={pq},\:{p},{q}\in\mathbb{Z}^{+} \backslash\left\{\mathrm{0},\:\mathrm{1}\right\} \\ $$$${n},{i}\in\mathbb{P} \\…
Question Number 71273 by eriga last updated on 13/Oct/19 Commented by $@ty@m123 last updated on 13/Oct/19 $${Welcome}\:{Eriga}. \\ $$$${Pl}.\:{use}\:{EDITOR}\:{option} \\ $$$${instead}\:{of}\:{FORUM}\:{to}\:{type} \\ $$$${math}\:{related}\:{material}. \\ $$$$…
Question Number 5705 by sanusihammed last updated on 24/May/16 Answered by FilupSmith last updated on 24/May/16 $${question}\:\left({b}\right) \\ $$$$\mathrm{from}\:\mathrm{previous}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{other}\:\mathrm{post}, \\ $$$$\mathrm{limit}\:\mathrm{can}\:\mathrm{be}\:\mathrm{simplified}\:\mathrm{to}: \\ $$$${L}=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{3}^{\mathrm{2}{x}} −\mathrm{1}}{\mathrm{3}^{\mathrm{2}{x}}…
Question Number 71216 by TawaTawa last updated on 13/Oct/19 Answered by mind is power last updated on 13/Oct/19 $$\Sigma\frac{\mathrm{n}^{\mathrm{2}} +\mathrm{x}}{\mathrm{n}!}=\Sigma\frac{\mathrm{n}^{\mathrm{2}} }{\mathrm{n}!}+\mathrm{x}\Sigma\frac{\mathrm{1}}{\mathrm{n}!} \\ $$$$\underset{\mathrm{n}\geqslant\mathrm{0}} {\sum}\frac{\mathrm{n}^{\mathrm{2}} }{\mathrm{n}!}=\mathrm{1}+\sum_{\mathrm{n}\geqslant\mathrm{2}}…
Question Number 136758 by mathlove last updated on 25/Mar/21 $$\:\:\mathrm{1}==>\:\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\pi}+\frac{\mathrm{1}}{\pi^{\mathrm{2}} }+\frac{\mathrm{1}}{\pi^{\mathrm{3}} }+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\pi^{{n}} }\right)=? \\ $$$$ \\ $$$$\:\mathrm{2}=>\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}+\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +\centerdot\centerdot\centerdot\centerdot+{n}^{\mathrm{2}} }{\mathrm{1}−{n}^{\mathrm{3}} }=? \\ $$…
Question Number 5637 by sanusihammed last updated on 23/May/16 $${Limit}\:\:\:\left[\frac{\mathrm{3}^{{n}+\mathrm{1}} \:−\:\mathrm{5}^{{n}+\mathrm{1}} }{\mathrm{3}^{{n}} \:−\:\mathrm{5}^{{n}} }\right] \\ $$$${x}\rightarrow\infty \\ $$$$ \\ $$$$ \\ $$$${Please}\:{help}.\:{Thanks} \\ $$ Answered…
Question Number 136700 by mathlove last updated on 25/Mar/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{n}^{{n}} +\mathrm{3}^{{n}} }{\mathrm{10}^{{n}} +\mathrm{3}^{{n}} }=? \\ $$ Commented by mathlove last updated on 25/Mar/21 $${thanks}…
Question Number 136701 by mathlove last updated on 25/Mar/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{3}^{{n}} −{n}!}{\mathrm{2}^{{n}} −{n}!}=? \\ $$ Commented by yutytfjh67ihd last updated on 25/Mar/21 Commented by mathlove…
Question Number 5616 by sanusihammed last updated on 22/May/16 $${Find}\: \\ $$$$ \\ $$$$\left[\mathrm{1}\:+\:\mathrm{3}{n}^{−\mathrm{1}} \right]^{{n}} \\ $$$$ \\ $$$${Limit}\:{as}\:{n}\:\rightarrow\infty \\ $$$$ \\ $$$$ \\ $$$${Please}\:{help}.…