Question Number 91133 by john santu last updated on 28/Apr/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\left({x}−\mathrm{1}\right)+\sqrt[{\mathrm{3}\:\:}]{\mathrm{1}−{x}}}{\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{1}−{x}^{\mathrm{2}} }}\:=\: \\ $$ Commented by john santu last updated on 28/Apr/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\left({x}−\mathrm{1}\right)+\left(\mathrm{1}−\frac{{x}}{\mathrm{3}}\right)}{\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{2}}\:\left(\mathrm{1}−\frac{{x}}{\mathrm{3}}\right)}\:=\:…
Question Number 25588 by behi.8.3.4.17@gmail.com last updated on 11/Dec/17 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\boldsymbol{{x}}−\boldsymbol{{tgx}}}{\boldsymbol{{x}}−\boldsymbol{{sinx}}}\right)=? \\ $$$$\boldsymbol{{l}}'\boldsymbol{{hopital}}\:\boldsymbol{{role}}\:\boldsymbol{{not}}\:\boldsymbol{{allowed}}! \\ $$ Commented by moxhix last updated on 12/Dec/17 https://math.stackexchange.com/questions/508733/lim-x-to0-fracx-sin-xx-tan-x-without-using-lhopital . Answered by…
Question Number 156640 by semanou last updated on 13/Oct/21 Answered by puissant last updated on 13/Oct/21 $$\left.{c}\right) \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}}{{tanx}}=\:\mathrm{1} \\ $$$$\left.{d}\right) \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}}{{sinx}}=\underset{{x}\rightarrow\mathrm{0}}…
Question Number 156611 by semanou last updated on 13/Oct/21 $${lim}\sqrt{{x}+\mathrm{5}} \\ $$ Commented by Rasheed.Sindhi last updated on 13/Oct/21 $${x}\rightarrow? \\ $$ Terms of Service…
Question Number 25495 by rita1608 last updated on 11/Dec/17 Commented by prakash jain last updated on 11/Dec/17 $$\mid{x}\mid=\begin{cases}{−{x}}&{{x}<\mathrm{0}}\\{{x}}&{{x}\geqslant\mathrm{0}}\end{cases} \\ $$$${f}\left({x}\right)=\begin{cases}{−{x}^{\mathrm{2}} }&{{x}<\mathrm{0}}\\{{x}^{\mathrm{2}} }&{{x}\geqslant\mathrm{0}}\end{cases} \\ $$$$\mathrm{clearly}\:\mathrm{it}\:\mathrm{differential}\:\mathrm{at}\:\mathrm{every}\:\mathrm{pt}\:\mathrm{other} \\…
Question Number 91020 by jagoll last updated on 27/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{sin}\:{x}\right)^{\frac{\mathrm{1}}{{x}}} \:?\: \\ $$ Commented by jagoll last updated on 28/Apr/20 $${it}\:{does}\:{mean}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{sin}\:{x}\right)^{\frac{\mathrm{1}}{{x}}} \:{DNE}? \\…
Question Number 156557 by mathlove last updated on 12/Oct/21 Commented by john_santu last updated on 13/Oct/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{3}^{{x}} −\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{3}^{{x}} +\mathrm{1}\right)}{\mathrm{1}−\mathrm{cos}\:{x}}.\frac{\sqrt{\mathrm{2}}+\sqrt{\mathrm{1}+\mathrm{cos}\:{x}}}{\mathrm{1}} \\ $$$$=\mathrm{4}\sqrt{\mathrm{2}}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{3}^{{x}} −\mathrm{1}\right)^{\mathrm{2}}…
Question Number 25460 by San Sophanethsan069 last updated on 10/Dec/17 Commented by behi.8.3.4.17@gmail.com last updated on 10/Dec/17 $$\mathrm{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{1}−\frac{\left(\mathrm{6x}\right)^{\mathrm{2}} }{\mathrm{2}}\right)−\left(\mathrm{1}−\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}\right)}{\mathrm{x}^{\mathrm{2}} }= \\ $$$$=−\frac{\mathrm{36}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}=−\frac{\mathrm{35}}{\mathrm{2}}\:.\blacksquare \\…
Question Number 90944 by john santu last updated on 27/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\:\mathrm{sin}\:{x}}{\mathrm{2sin}\:^{\mathrm{2}} \mathrm{3}{x}−{x}^{\mathrm{2}} \:\mathrm{cos}\:{x}}\:? \\ $$ Commented by john santu last updated on 27/Apr/20 Commented…
Question Number 25379 by A1B1C1D1 last updated on 09/Dec/17 $$\underset{\mathrm{x}\:\rightarrow\:\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\left(\mathrm{1}\:+\:\mathrm{x}\right)^{\mathrm{a}} \:−\:\mathrm{1}}{\mathrm{x}}\right)\:\mathrm{for}\:\mathrm{a}\:\in\:\mathbb{R} \\ $$$$ \\ $$$$\mathrm{Don}'\mathrm{t}\:\mathrm{using}\:\mathrm{L}'\mathrm{hospital}\:\mathrm{rules}. \\ $$ Answered by Rasheed.Sindhi last updated on 10/Dec/17…