Question Number 137157 by mathlove last updated on 30/Mar/21 Commented by mathlove last updated on 30/Mar/21 $${with}\:{out}\:{macloreen}\:{sirees}\:{and}\:{H}-{pital}\:{rools} \\ $$ Commented by mathlove last updated on…
Question Number 71513 by aliesam last updated on 16/Oct/19 Commented by kaivan.ahmadi last updated on 16/Oct/19 $$×\frac{\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}+\sqrt{{x}−\mathrm{1}}}{\:\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}+\sqrt{{x}−\mathrm{1}}}={lim}_{{x}\rightarrow+\infty} \frac{{x}^{\mathrm{2}} +\mathrm{2}}{\:\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}+\sqrt{{x}−\mathrm{1}}}= \\ $$$$\equiv{lim}_{{x}\rightarrow+\infty} \frac{{x}^{\mathrm{2}}…
Question Number 71362 by malwaan last updated on 14/Oct/19 $$\boldsymbol{\mathrm{please}}\:\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{lim}}}\frac{\boldsymbol{{x}}−\boldsymbol{{sinx}}}{\boldsymbol{{x}}^{\mathrm{3}} }\:=\frac{\mathrm{1}}{\mathrm{6}}\:\boldsymbol{{by}}\:\boldsymbol{{using}} \\ $$$$\boldsymbol{{x}}=\mathrm{3}\boldsymbol{{y}}\:\boldsymbol{{and}}\: \\ $$$$\boldsymbol{{sin}}\mathrm{3}\boldsymbol{{y}}=\mathrm{3}\boldsymbol{{siny}}−\mathrm{4}\boldsymbol{{sin}}^{\mathrm{3}} \boldsymbol{{y}} \\ $$ Terms of Service Privacy…
Question Number 71360 by 20190927 last updated on 14/Oct/19 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\sqrt{\mathrm{1}+\mathrm{2x}^{\mathrm{4}} }\mathrm{cos}\:\left(\sqrt{\mathrm{2}}\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{5}} \mathrm{ln}\:\left(\mathrm{1}−\mathrm{2x}^{\mathrm{3}} \right)} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 5821 by FilupSmith last updated on 30/May/16 $${L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{x}^{{x}} \\ $$ Answered by bahmanfeshki last updated on 27/Feb/17 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:{e}^{{x}\mathrm{ln}\:{x}} =\underset{{x}\rightarrow\mathrm{0}^{+} }…
Question Number 136854 by Raxreedoroid last updated on 26/Mar/21 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} {k}×\:^{{n}−\mathrm{1}} {C}_{{k}−\mathrm{1}} \right)=? \\ $$$$\:^{{n}} {C}_{{r}} =\frac{{n}!}{{r}!\left({n}−{r}\right)!} \\ $$ Commented by mr…
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}}…