Category: Limits

Question Number 156557 by mathlove last updated on 12/Oct/21 Commented by john_santu last updated on 13/Oct/21 $$\underset{x\to 0}{\lim }\frac{{(3^x-1)}^2(3^x+1)}{1-\cos x}.\frac{\sqrt{2}+\sqrt{1+\cos x}}{1}$$$$=\mathrm{4}\sqrt{\mathrm{2}}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{3}^{{x}} −\mathrm{1}\right)^{\mathrm{2}}…

Question Number 90944 by john santu last updated on 27/Apr/20 $$\underset{x\to 0}{\lim }\frac{x\sin x}{2\sin {}^{2}3x-x^2\cos x}?$$ Commented by john santu last updated on 27/Apr/20 Commented…

Question Number 156434 by cortano last updated on 11/Oct/21 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 25300 by SAGARSTARK last updated on 07/Dec/17 Commented by prakash jain last updated on 08/Dec/17 $$\mathrm{You}\mathrm{may}\mathrm{also}\mathrm{want}\mathrm{to}\mathrm{see}$$$$\mathrm{Q}2088.\mathrm{Different}\mathrm{but}\mathrm{similar}$$$$\mathrm{question}.$$ Commented…

Question Number 90788 by jagoll last updated on 26/Apr/20 $$\underset{x\to -\mathrm{\infty }}{\lim }{\left(\frac{x+2}{x+1}\right)}^{\frac{x}{2}}$$ 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}}}…