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Category: Limits

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}}…

Question-87105

Question Number 87105 by Chi Mes Try last updated on 02/Apr/20 Commented by mathmax by abdo last updated on 03/Apr/20 $${let}\:{f}\left({x}\right)=\frac{{x}}{{x}−\mathrm{1}}−\frac{\mathrm{1}}{{lnx}}\:\Rightarrow{f}\left({x}\right)=\frac{{xln}\left({x}\right)−{x}+\mathrm{1}}{\left({x}−\mathrm{1}\right){ln}\left({x}\right)}\:{we}\:{do}\:{the}\:{changement} \\ $$$${x}−\mathrm{1}\:={t}\:\Rightarrow{f}\left({x}\right)=\frac{\left({t}+\mathrm{1}\right){ln}\left(\mathrm{1}+{t}\right)+\mathrm{1}−\left({t}+\mathrm{1}\right)}{{tln}\left(\mathrm{1}+{t}\right)}={g}\left({t}\right) \\ $$$$=\frac{\left({t}+\mathrm{1}\right){ln}\left(\mathrm{1}+{t}\right)−{t}}{{tln}\left(\mathrm{1}+{t}\right)}\:\:\left({x}\rightarrow\mathrm{1}\:\Rightarrow{t}\rightarrow\mathrm{0}\right)\:{so}…