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Category: Limits

Question-176672

Question Number 176672 by youssefelaour last updated on 24/Sep/22 Answered by Mathspace last updated on 25/Sep/22 $${we}\:{do}\:{the}\:{changement}\:{x}−\frac{\pi}{\mathrm{2}}={t} \\ $$$${so}\:{l}\left({x}\right)=\frac{\left(\mathrm{1}−{cost}\right)\left(\mathrm{1}−{cos}^{\mathrm{2}} {t}\right)….\left(\mathrm{1}−{cos}^{{n}} {t}\right)}{{sin}^{\mathrm{2}{n}} {t}} \\ $$$${but}\:\mathrm{1}−{cost}\sim\frac{{t}^{\mathrm{2}} }{\mathrm{2}}…

Question-176673

Question Number 176673 by cortano1 last updated on 24/Sep/22 Answered by mr W last updated on 24/Sep/22 $$=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{14}\left({x}^{\mathrm{6}} −\mathrm{1}\right)^{\frac{\mathrm{6}}{\mathrm{7}}} }{\mathrm{15}{x}^{\frac{\mathrm{26}}{\mathrm{5}}} }=\mathrm{0} \\ $$ Terms…

lim-x-1-x-1-x-2-1-

Question Number 111100 by bobhans last updated on 02/Sep/20 $$\underset{{x}\rightarrow\mathrm{1}^{+} } {\mathrm{lim}}\:\frac{\mathrm{x}−\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}\:? \\ $$ Answered by 1549442205PVT last updated on 02/Sep/20 $$\underset{\mathrm{x}\rightarrow\mathrm{1}^{+} } {\mathrm{lim}}\:\frac{\mathrm{x}−\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}}…

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

Question Number 176638 by cortano1 last updated on 23/Sep/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{x}\right)−\mathrm{sin}\:\left(\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{x}\right)−\mathrm{cos}\:\left(\mathrm{x}^{\mathrm{2}} \right)\right)}=? \\ $$ Answered by a.lgnaoui last updated on 23/Sep/22…

Question-176589

Question Number 176589 by Ar Brandon last updated on 22/Sep/22 Answered by Peace last updated on 23/Sep/22 $$\mid{u}_{{n}} \left({z}\right)\mid=\frac{\mid{z}\mid^{{n}} }{\mid\mathrm{1}+{z}^{\mathrm{2}{n}+\mathrm{1}} \mid}\leqslant\frac{\mid{z}\mid^{{n}} }{\mathrm{1}−\mid{z}\mid^{\mathrm{2}{n}+\mathrm{1}} },\:\mid{z}\mid<\mathrm{1} \\ $$$$\exists{n}\in\mathbb{N}\mid\forall{m}\geqslant{n}\:\:\:\:\mid{z}\mid\:\:\:<\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow.\mid{U}_{{m}}…