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Question Number 87799 by M±th+et£s last updated on 06/Apr/20 $${f}\left({x}\right)=\begin{cases}{{ax}^{\mathrm{2}} +{bx}\:\:\:\:\:\:−\mathrm{1}\leqslant{x}\leqslant\mathrm{0}}\\{{cx}^{\mathrm{2}} +{d}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}<{x}\leqslant\frac{\mathrm{1}}{\mathrm{2}}}\\{{bx}+{d}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}<{x}\leqslant\mathrm{1}}\end{cases} \\ $$$${f}\left({x}\right)\:{is}\:{continuous}\:{on}\left[−\mathrm{1},\mathrm{1}\right] \\ $$$${prove}\:{d}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{c}=\mathrm{2}{b} \\ $$ Commented by john santu last…
Question Number 22203 by Joel577 last updated on 13/Oct/17 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{e}^{{x}} \:\mathrm{cos}\:{x} \\ $$ Commented by squidward last updated on 17/Oct/17 $${undefined} \\ $$ Answered…
Question Number 22165 by A1B1C1D1 last updated on 12/Oct/17 Answered by ajfour last updated on 13/Oct/17 $${let}\:\:\frac{{x}}{\mathrm{1}−{x}^{\mathrm{2}} }\:={t}\:\:\:\:\Rightarrow\:{x}^{\mathrm{2}} =\mathrm{1}−\frac{{x}}{{t}} \\ $$$${L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}+\frac{{x}}{{t}}−\mathrm{2}\left(\mathrm{1}−\frac{{t}^{\mathrm{2}} }{\mathrm{2}}+\frac{{t}^{\mathrm{4}} }{\mathrm{24}}−….\right)}{\mathrm{2}{x}^{\mathrm{4}} }\right)…
Question Number 87690 by jagoll last updated on 05/Apr/20 $$\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)}\:=…
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 $$\:\:\underset{{x}\rightarrow\mathrm{y}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{e}^{\mathrm{x}} \right)−\mathrm{sin}\:\left(\mathrm{e}^{\mathrm{y}}…
Question Number 87462 by mathocean1 last updated on 04/Apr/20 $$\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 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{x}−\mathrm{1}\right)}{\mathrm{3x}−\mathrm{3}}\:? \\…
Question Number 87358 by john santu last updated on 04/Apr/20 $$\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…
Question Number 21811 by drbl.gnbd last updated on 04/Oct/17 $${a}_{\mathrm{1}} =\mathrm{1},\:{a}_{{n}+\mathrm{1}} =\frac{{a}_{{n}} }{\:\sqrt{{a}_{{n}} +{n}+\mathrm{1}}} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{a}_{{n}} =? \\ $$ Commented by Ranjiy kumar…
Question Number 87243 by john santu last updated on 03/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}−\:\mathrm{sin}\:{x}}{\:\sqrt{\left(\mathrm{1}−\mathrm{cos}\:{x}\right)^{{p}} }}\:=\:{k}\: \\ $$$${k}\:=\:{constant}\:,\:\mathrm{find}\:\mathrm{p}\: \\ $$ Commented by jagoll last updated on 04/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}}…