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Category: Limits

Question-22165

Question Number 22165 by A1B1C1D1 last updated on 12/Oct/17 Answered by ajfour last updated on 13/Oct/17 $${let}\:\:\frac{{x}}{\mathrm{1}−{x}^{\mathrm{2}} }\:={t}\:\:\:\:\Rightarrow\:{x}^{\mathrm{2}} =\mathrm{1}−\frac{{x}}{{t}} \\ $$$${L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}+\frac{{x}}{{t}}−\mathrm{2}\left(\mathrm{1}−\frac{{t}^{\mathrm{2}} }{\mathrm{2}}+\frac{{t}^{\mathrm{4}} }{\mathrm{24}}−….\right)}{\mathrm{2}{x}^{\mathrm{4}} }\right)…

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

Question Number 87690 by jagoll last updated on 05/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2sin}\:\mathrm{x}−\mathrm{sin}\:\mathrm{2x}}{\mathrm{x}−\mathrm{sin}\:\mathrm{x}} \\ $$ Commented by jagoll last updated on 05/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}\left(\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{6}}\right)−\left(\mathrm{2x}−\frac{\mathrm{8x}^{\mathrm{3}} }{\mathrm{6}}\right)}{\mathrm{x}−\left(\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{6}}\right)}\:=…

lim-x-y-sin-e-x-sin-e-y-x-y-

Question Number 153154 by liberty last updated on 05/Sep/21 $$\:\:\underset{{x}\rightarrow{y}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left({e}^{{x}} \right)−\mathrm{sin}\:\left({e}^{{y}} \right)}{{x}−{y}}=? \\ $$ Answered by bramlexs22 last updated on 05/Sep/21 $$\:\:\underset{{x}\rightarrow\mathrm{y}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{e}^{\mathrm{x}} \right)−\mathrm{sin}\:\left(\mathrm{e}^{\mathrm{y}}…

Calculate-lim-x-1-f-x-sin-x-1-3x-3-please-detail-sirs-

Question Number 87462 by mathocean1 last updated on 04/Apr/20 $$\mathrm{Calculate}\:\:\:\:\:\:\:\:\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{1}} {\mathrm{m}f}\left({x}\right)=\frac{{sin}\left({x}−\mathrm{1}\right)}{\mathrm{3}{x}−\mathrm{3}} \\ $$$${please}\:{detail}\:{sirs} \\ $$ Commented by jagoll last updated on 04/Apr/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{x}−\mathrm{1}\right)}{\mathrm{3x}−\mathrm{3}}\:? \\…

what-is-the-number-of-integral-values-of-y-for-which-lim-x-0-y-2-10y-24-sin-1-x-y-2-10y-24-sin-2-x-does-not-exist-

Question Number 87358 by john santu last updated on 04/Apr/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\: \\ $$$$\mathrm{integral}\:\mathrm{values}\:\mathrm{of}\:\mathrm{y}\:\mathrm{for}\:\mathrm{which}? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{y}^{\mathrm{2}} +\mathrm{10y}−\mathrm{24}\:\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)}{\mathrm{y}^{\mathrm{2}} +\mathrm{10y}\:−\mathrm{24}\:\mathrm{sin}\:\left(\frac{\mathrm{2}}{\mathrm{x}}\right)}\: \\ $$$$\mathrm{does}\:\mathrm{not}\:\mathrm{exist} \\ $$ Terms of Service…

lim-x-0-e-x-e-x-2-x-2-

Question Number 87153 by jagoll last updated on 03/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{e}^{\mathrm{x}} +\mathrm{e}^{−\mathrm{x}} −\mathrm{2}}{\mathrm{x}^{\mathrm{2}} } \\ $$ Commented by john santu last updated on 03/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}}…