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…
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Question Number 156421 by cortano last updated on 11/Oct/21 Commented by MJS_new last updated on 11/Oct/21 $$\mathrm{2} \\ $$ Commented by cortano last updated on…
Question Number 25300 by SAGARSTARK last updated on 07/Dec/17 Commented by prakash jain last updated on 08/Dec/17 $$\mathrm{You}\:\mathrm{may}\:\mathrm{also}\:\mathrm{want}\:\mathrm{to}\:\mathrm{see} \\ $$$$\mathrm{Q2088}.\:\mathrm{Different}\:\mathrm{but}\:\mathrm{similar} \\ $$$$\mathrm{question}. \\ $$ Commented…
Question Number 25287 by 9931558112 last updated on 07/Dec/17 $${limit}_{{x}−\mathrm{0}^{−} } \mathrm{sin}\:\left({log}_{{e}} {x}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 90788 by jagoll last updated on 26/Apr/20 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\left(\frac{{x}+\mathrm{2}}{{x}+\mathrm{1}}\right)^{\frac{{x}}{\mathrm{2}}} \\ $$ Commented by mathmax by abdo last updated on 26/Apr/20 $${let}\:{f}\left({x}\right)=\left(\frac{{x}+\mathrm{2}}{{x}+\mathrm{1}}\right)^{\frac{{x}}{\mathrm{2}}} \:\:\Rightarrow{f}\left({x}\right)\:=_{{x}=−{t}} \:\:\left(\frac{−{t}+\mathrm{2}}{−{t}+\mathrm{1}}\right)^{−\frac{{t}}{\mathrm{2}}}…