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Category: Limits

lim-x-2-3-x-9-x-2-

Question Number 149871 by ArielVyny last updated on 07/Aug/21 $${lim}_{{x}\rightarrow\mathrm{2}} \frac{\mathrm{3}^{{x}!} −\mathrm{9}}{{x}−\mathrm{2}} \\ $$ Answered by Ar Brandon last updated on 08/Aug/21 $$\mathscr{L}=\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\mathrm{3}^{{x}!} −\mathrm{9}}{{x}−\mathrm{2}}…

lim-x-1-2x-3-x-1-64-x-3-1-

Question Number 84330 by M±th+et£s last updated on 11/Mar/20 $$\underset{{x}\rightarrow\mathrm{1}} {{lim}}\frac{\left(\mathrm{2}{x}^{\mathrm{3}} +{x}+\mathrm{1}\right)−\mathrm{64}}{{x}^{\mathrm{3}} −\mathrm{1}} \\ $$ Commented by M±th+et£s last updated on 11/Mar/20 $${typo}\:\left(\mathrm{2}{x}^{\mathrm{3}} +{x}+\mathrm{1}\right)^{\mathrm{3}} \\…

lim-x-a-x-1-2-a-1-2-x-a-k-a-gt-0-lim-x-a-x-1-3-a-1-3-x-2-a-2-

Question Number 84283 by jagoll last updated on 11/Mar/20 $$\underset{{x}\rightarrow\mathrm{a}} {\mathrm{lim}}\:\frac{\left(\mid\mathrm{x}\mid−\mathrm{1}\right)^{\mathrm{2}} −\left(\mid\mathrm{a}\mid−\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{x}−\mathrm{a}}\:=\:\mathrm{k}\:,\:\mathrm{a}>\mathrm{0} \\ $$$$\underset{{x}\rightarrow\mathrm{a}} {\mathrm{lim}}\:\frac{\left(\mid\mathrm{x}\mid−\mathrm{1}\right)^{\mathrm{3}} −\left(\mid\mathrm{a}\mid−\mathrm{1}\right)^{\mathrm{3}} }{\mathrm{x}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} }\:=\: \\ $$$$ \\ $$ Answered…

Question-149782

Question Number 149782 by iloveisrael last updated on 07/Aug/21 Answered by john_santu last updated on 07/Aug/21 $$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\mathrm{6}{x}+\mathrm{2sin}\:\mathrm{6}{x}\mathrm{cos}\:\mathrm{4}{x}−\left(\mathrm{3sin}\:\mathrm{6}{x}−\mathrm{4sin}\:^{\mathrm{3}} \mathrm{6}{x}\right)}{\mathrm{3sin}\:{x}−\left(\mathrm{3sin}\:{x}−\mathrm{4sin}\:^{\mathrm{3}} {x}\right)} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{−\mathrm{2sin}\:\mathrm{6}{x}+\mathrm{2sin}\:\mathrm{6}{x}\:\mathrm{cos}\:\mathrm{4}{x}+\mathrm{4sin}\:^{\mathrm{3}} \mathrm{6}{x}\:}{\mathrm{4sin}\:^{\mathrm{3}} {x}}…

Question-149700

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…

lim-x-0-sin-x-x-sin-x-x-sin-x-

Question Number 18627 by Arnab Maiti last updated on 26/Jul/17 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\right)^{\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}−\mathrm{sin}\:\mathrm{x}}} \\ $$ Commented by Arnab Maiti last updated on 26/Jul/17 $$\mathrm{Please}\:\mathrm{help}. \\ $$…

Without-using-L-Hospital-s-rule-prove-that-lim-x-0-sin-x-x-1-

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}.…