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Category: Limits

lim-x-5x-4-10x-2-1-3x-3-10x-2-50-

Question Number 28770 by Rasheed.Sindhi last updated on 30/Jan/18 $$\underset{{x}\rightarrow+\infty} {{lim}}\:\frac{\mathrm{5}{x}^{\mathrm{4}} −\mathrm{10}{x}^{\mathrm{2}} +\mathrm{1}}{−\mathrm{3}{x}^{\mathrm{3}} +\mathrm{10}{x}^{\mathrm{2}} +\mathrm{50}} \\ $$ Commented by Cheyboy last updated on 30/Jan/18 $$\underset{{x}\rightarrow+\infty\:}…

lim-x-2021x-2-6x-1021x-3-5x-1-3-

Question Number 159837 by tounghoungko last updated on 21/Nov/21 $$\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\sqrt{\mathrm{2021}{x}^{\mathrm{2}} −\mathrm{6}{x}}\:+\sqrt[{\mathrm{3}}]{\mathrm{1021}{x}^{\mathrm{3}} −\mathrm{5}{x}}\:=? \\ $$ Answered by kaivan.ahmadi last updated on 24/Nov/21 $$\sim{lim}\sqrt{\mathrm{2021}}\mid{x}−\frac{−\mathrm{6}}{\mathrm{2}×\mathrm{2021}}\mid+\sqrt[{\mathrm{3}}]{\mathrm{1021}}\mid{x}\mid= \\ $$$${lim}\sqrt{\mathrm{2021}}\left(−{x}−\frac{\mathrm{3}}{\mathrm{2021}}\right)−\sqrt[{\mathrm{3}}]{\mathrm{1021}}{x}=+\infty…

Montrer-que-la-suite-de-finie-par-u-n-k-1-n-x-k-k-est-une-suite-de-Cauchy-

Question Number 159796 by Ar Brandon last updated on 21/Nov/21 $$\mathrm{Montrer}\:\mathrm{que}\:\mathrm{la}\:\mathrm{suite}\:\mathrm{d}\acute {\mathrm{e}finie}\:\mathrm{par}\: \\ $$$${u}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{x}^{{k}} }{{k}}\:\mathrm{est}\:\mathrm{une}\:\mathrm{suite}\:\mathrm{de}\:\mathrm{Cauchy}. \\ $$ Answered by alcohol last updated…

negative-number-or-

Question Number 28698 by Rasheed.Sindhi last updated on 29/Jan/18 $$\frac{\infty}{\mathrm{negative}\:\mathrm{number}}=? \\ $$$$\:\infty\:\:\:\:\:\:\:\:\:\:\mathrm{or}\:\:\:\:\:\:\:\:\:−\infty\:\:? \\ $$ Commented by prakash jain last updated on 29/Jan/18 $$−\infty \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{−}…

lim-x-0-tan-x-sin-x-2-x-sin-x-tan-x-

Question Number 159754 by cortano last updated on 20/Nov/21 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\sqrt{\mathrm{tan}\:{x}}\:+\:\sqrt{\mathrm{sin}\:{x}}\:−\mathrm{2}\sqrt{{x}}}{\:\sqrt{\mathrm{sin}\:{x}}\:−\:\sqrt{\mathrm{tan}\:{x}}\:}\:=\:? \\ $$ Answered by bobhans last updated on 21/Nov/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\sqrt{\mathrm{tan}\:\mathrm{x}}\:+\sqrt{\mathrm{sin}\:\mathrm{x}}−\mathrm{2}\sqrt{\mathrm{x}}}{\:\sqrt{\mathrm{sin}\:\mathrm{x}}−\sqrt{\mathrm{tan}\:\mathrm{x}}}\: \\…