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Category: Limits

lim-x-1-x-4x-2-6x-2-2x-dx-5x-

Question Number 169273 by cortano1 last updated on 27/Apr/22 $$\:\:\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\int_{\mathrm{1}} ^{\:{x}} \left(\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{6}{x}−\mathrm{2}}−\mathrm{2}{x}\right){dx}}{\mathrm{5}{x}}\:=? \\ $$ Answered by qaz last updated on 28/Apr/22 $$\underset{\mathrm{x}\rightarrow+\infty} {\mathrm{lim}}\frac{\int_{\mathrm{1}}…

if-a-b-gt-1-lim-x-0-ln-b-x-ax-

Question Number 103654 by Study last updated on 16/Jul/20 $$\:{if}\:{a},{b}>\mathrm{1}\:\:{li}\underset{{x}\rightarrow\mathrm{0}^{+} } {{m}}\frac{{ln}\left({b}−{x}\right)}{{ax}}=??? \\ $$ Answered by Worm_Tail last updated on 16/Jul/20 $$\:\:\:\:\:\:{li}\underset{{x}\rightarrow\mathrm{0}^{+} } {{m}}\frac{{ln}\left({b}−{x}\right)}{{ax}}={lim}\left(\frac{\mathrm{1}}{{a}}{ln}\left({b}−{x}\right)^{\frac{\mathrm{1}}{{x}}} \right)…

find-for-arbitrary-0-the-limit-lim-n-1-2-3-n-n-n-1-

Question Number 169166 by infinityaction last updated on 25/Apr/22 $$\:\:\:\:\:\:\:\:\mathrm{find}\:\mathrm{for}\:\mathrm{arbitrary}\:\alpha\geqslant\mathrm{0}\:\mathrm{the}\:\mathrm{limit}\: \\ $$$$\:\:\:\underset{\boldsymbol{\mathrm{n}}\rightarrow+\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{1}^{\alpha} +\mathrm{2}^{\alpha} +\mathrm{3}^{\alpha} +……\mathrm{n}^{\alpha} }{\mathrm{n}^{\alpha} }−\frac{\mathrm{n}}{\mathrm{1}+\alpha}\right) \\ $$ Commented by safojontoshtemirov last updated…

lim-x-pi-picos2x-1-1-cosx-

Question Number 169148 by mathlove last updated on 25/Apr/22 $$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\frac{\pi{cos}\mathrm{2}{x}−\mathrm{1}}{\mathrm{1}+{cosx}}=? \\ $$ Commented by infinityaction last updated on 25/Apr/22 $$\:\:\:\:\:{p}\:=\:\:\:\frac{\pi\mathrm{cos}\:\mathrm{2}\pi−\mathrm{1}}{\mathrm{1}+\mathrm{cos}\:\pi} \\ $$$$\:\:\:\:\:\:{p}\:\:=\:\:\frac{\pi×\mathrm{1}−\mathrm{1}}{\mathrm{1}−\mathrm{1}}\:=\:\frac{\pi−\mathrm{1}}{\mathrm{0}}\:=\:\infty \\ $$$$…