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Category: Limits

lim-n-2-2-3-2-5-2-n-1-3-2-3-4-3-n-1-n-2-1-4-

Question Number 36969 by rahul 19 last updated on 07/Jun/18 $$\left[\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{2}.\mathrm{2}^{\mathrm{3}} .\mathrm{2}^{\mathrm{5}} …..\mathrm{2}^{\mathrm{n}−\mathrm{1}} .\mathrm{3}^{\mathrm{2}} .\mathrm{3}^{\mathrm{4}} …..\mathrm{3}^{\mathrm{n}} \right)^{\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{1}}} \right]^{\mathrm{4}} =? \\ $$ Answered by…

lim-n-nsin-2pi-1-n-2-n-N-

Question Number 36953 by rahul 19 last updated on 07/Jun/18 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{nsin}\:\left(\mathrm{2}\pi\sqrt{\mathrm{1}+\mathrm{n}^{\mathrm{2}} }\:\right)\:,\left(\:\mathrm{n}\in\mathbb{N}\right). \\ $$ Commented by rahul 19 last updated on 07/Jun/18 Thank you Prof ���� Commented…

lim-x-0-5e-x-5e-x-10-4x-2-

Question Number 168014 by mathlove last updated on 31/Mar/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{5}{e}^{{x}} +\mathrm{5}{e}^{−{x}} −\mathrm{10}}{\mathrm{4}{x}^{\mathrm{2}} }=? \\ $$ Answered by som(math1967) last updated on 01/Apr/22 $$\:\:\frac{\mathrm{5}{e}^{{x}} +\frac{\mathrm{5}}{{e}^{{x}}…

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

Question Number 168009 by mathlove last updated on 31/Mar/22 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}+\mathrm{3}{x}}{\:\sqrt{{x}^{\mathrm{2}} +{x}−\mathrm{5}}+{x}}=? \\ $$ Answered by nurtani last updated on 31/Mar/22 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}+\mathrm{3}{x}}{\:\sqrt{{x}^{\mathrm{2}}…

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

Question Number 168004 by mathlove last updated on 31/Mar/22 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{16}{x}+\mathrm{1}}−\mathrm{2}{x}+\mathrm{3}=? \\ $$ Answered by nurtani last updated on 31/Mar/22 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{16}{x}+\mathrm{1}}−\mathrm{2}{x}+\mathrm{3}\:=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{4}{x}^{\mathrm{2}}…

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

Question Number 167980 by mathlove last updated on 31/Mar/22 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{16}{x}+\mathrm{1}}−\mathrm{2}{x}+\mathrm{3}=? \\ $$ Commented by cortano1 last updated on 31/Mar/22 $$=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{2}\left({x}−\frac{\mathrm{16}}{\mathrm{8}}\right)−\mathrm{2}{x}+\mathrm{3} \\ $$$$=\:−\mathrm{4}+\mathrm{3}=−\mathrm{1}…