Category: Limits

Question Number 149700 by Lekhraj last updated on 06/Aug/21 Commented by iloveisrael last updated on 07/Aug/21 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\left(\mathrm{x}+\mathrm{x}\sqrt{\mathrm{1}+\mathrm{4x}^{−\mathrm{1}} }\right) \\ $$$$=\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}x}\left(\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{4x}^{−\mathrm{1}} }\:\right) \\ $$$$=−\infty×\mathrm{2}\:=\:−\infty…

Question Number 18611 by Arnab Maiti last updated on 25/Jul/17 $$\mathrm{Without}\:\mathrm{using}\:\mathrm{L}\:\mathrm{Hospital}'\mathrm{s} \\ $$$$\mathrm{rule}\:\mathrm{prove}\:\mathrm{that}\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}=\mathrm{1} \\ $$ Commented by Arnab Maiti last updated on 25/Jul/17 $$\mathrm{I}\:\mathrm{have}\:\mathrm{no}\:\mathrm{NCERT}\:\mathrm{books}.…

Question Number 84130 by mahdi last updated on 09/Mar/20 $$\underset{{x}\rightarrow+\infty} {\mathrm{lim}x}\left(\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}}−\mathrm{2}\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}}+\mathrm{x}\right) \\ $$ Commented by MJS last updated on 10/Mar/20 $$\mathrm{let}\:{x}=\frac{\mathrm{1}}{{t}} \\ $$$$\underset{{t}\rightarrow\mathrm{0}^{+}…

Question Number 149660 by fotosy2k last updated on 06/Aug/21 Answered by JDamian last updated on 06/Aug/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{a}^{{n}+\mathrm{1}} }{{a}^{{n}} +{b}^{{n}} }+\frac{{b}^{{n}+\mathrm{1}} }{{a}^{{n}} +{b}^{{n}} }\right)= \\…

Question Number 149637 by mnjuly1970 last updated on 06/Aug/21 Answered by iloveisrael last updated on 06/Aug/21 $$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{1}+\mathrm{x}^{−\mathrm{1}} +\mathrm{x}^{−\mathrm{4}} }\:−\mathrm{x}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{x}^{−\mathrm{1}} \right)}{\mathrm{x}} \\ $$$$=\:\underset{{x}\rightarrow\infty}…