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Category: Limits

lim-x-6-8xsin-3-x-

Question Number 83401 by jagoll last updated on 02/Mar/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{6}−\mathrm{8xsin}\:\left(\frac{\mathrm{3}}{\mathrm{x}}\right)\right)=\:? \\ $$ Commented by mathmax by abdo last updated on 02/Mar/20 $$\mathrm{6}−\mathrm{8}{x}\:{sin}\left(\frac{\mathrm{3}}{{x}}\right)\sim\mathrm{6}−\mathrm{8}{x}×\frac{\mathrm{3}}{{x}}\:\Rightarrow{lim}_{{x}\rightarrow\infty} \left(\mathrm{6}−\mathrm{8}{x}\:{sin}\left(\frac{\mathrm{3}}{{x}}\right)\right)=\mathrm{6}−\mathrm{24}=−\mathrm{18} \\…

lim-x-0-1-cos-x-x-

Question Number 83361 by john santu last updated on 01/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{x}\right)}{\:\sqrt{\mathrm{x}}}\:=\: \\ $$ Commented by john santu last updated on 01/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}^{+} }…

lim-x-0-e-2x-1-ax-x-2-1-bx-

Question Number 83329 by john santu last updated on 01/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{e}^{−\mathrm{2x}} −\left(\mathrm{1}+\mathrm{ax}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:\left(\mathrm{1}+\mathrm{bx}\right)}\:=\:? \\ $$ Commented by jagoll last updated on 01/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{bx}}\:×\:\underset{{x}\rightarrow\mathrm{0}}…

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

Question Number 83323 by john santu last updated on 01/Mar/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\left(\mathrm{3x}−\mathrm{2}\right)\left(\mathrm{x}−\sqrt{\mathrm{2}}\right)}\:−\:\mathrm{x}\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}\:=? \\ $$$$ \\ $$ Commented by abdomathmax last updated on 01/Mar/20 $${let}\:{f}\left({x}\right)=\sqrt{\left(\mathrm{3}{x}−\mathrm{2}\right)\left({x}−\sqrt{\mathrm{2}}\right)}−{x}\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}} \\…

lim-x-0-x-16-1-4-x-8-1-3-4-x-2-2x-

Question Number 148848 by EDWIN88 last updated on 31/Jul/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{4}}]{{x}+\mathrm{16}}\:\sqrt[{\mathrm{3}}]{{x}+\mathrm{8}}\:−\mathrm{4}}{{x}^{\mathrm{2}} +\mathrm{2}{x}}\:=?\: \\ $$ Answered by mathmax by abdo last updated on 01/Aug/21 $$\mathrm{f}\left(\mathrm{x}\right)=\frac{\left(\mathrm{x}+\mathrm{16}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} \left(\mathrm{x}+\mathrm{8}\right)^{\frac{\mathrm{1}}{\mathrm{3}}}…

Question-83287

Question Number 83287 by Power last updated on 29/Feb/20 Answered by mr W last updated on 29/Feb/20 $$\mathrm{sin}\:{x}={x}−\frac{{x}^{\mathrm{3}} }{\mathrm{3}!}+\frac{{x}^{\mathrm{5}} }{\mathrm{5}!}−….. \\ $$$$\frac{\mathrm{sin}\:{x}}{{x}}=\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\mathrm{3}!}+\frac{{x}^{\mathrm{4}} }{\mathrm{5}!}−….. \\…

Question-148819

Question Number 148819 by mathlove last updated on 31/Jul/21 Answered by liberty last updated on 31/Jul/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}}{\left(\mathrm{1}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{n}}\right)−\left(\mathrm{1}+\frac{\mathrm{x}}{\mathrm{n}}\right)}\:= \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}}{\frac{\mathrm{x}}{\mathrm{n}}\left(\mathrm{x}−\mathrm{1}\right)}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{n}}{\mathrm{x}−\mathrm{1}}=−\:\mathrm{n} \\ $$…