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Category: Limits

Question-169294

Question Number 169294 by cortano1 last updated on 28/Apr/22 Commented by qaz last updated on 28/Apr/22 $$\mathrm{Same}\:\mathrm{as}\::\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\mathrm{tan}\:\mathrm{x}−\mathrm{tan}\:\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{7}} }=−\frac{\mathrm{1}}{\mathrm{14}} \\ $$ Commented by cortano1 last…

lim-n-2-n-sin-pi-2-n-

Question Number 103749 by bobhans last updated on 17/Jul/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{2}^{{n}} \:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}^{{n}} }\right)\:=\:? \\ $$ Answered by bramlex last updated on 17/Jul/20 $${set}\:{x}\:=\:\frac{\pi}{\mathrm{2}^{{n}} }\:\Rightarrow\mathrm{2}^{{n}} \:=\:\frac{\pi}{{x}}\:;{x}\rightarrow\mathrm{0}…

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)…