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Category: Limits

Question-42895

Question Number 42895 by Joel578 last updated on 04/Sep/18 Commented by Joel578 last updated on 04/Sep/18 $$\mathrm{For}\:\mathrm{question}\:\left({c}\right), \\ $$$$\mathrm{the}\:\mathrm{limit}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{exist}\:\mathrm{or}\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:{f}\left({x}\right)\:=\:\mathrm{1}\:? \\ $$ Answered by MJS…

Derive-Leibniz-s-formula-fg-n-x-0-k-0-n-C-n-k-f-k-x-0-g-n-k-x-0-

Question Number 108349 by Ar Brandon last updated on 16/Aug/20 $$\mathrm{Derive}\:\mathrm{Leibniz}'\mathrm{s}\:\mathrm{formula}\:: \\ $$$$\left(\mathrm{fg}\right)^{\left(\mathrm{n}\right)} \left(\mathrm{x}_{\mathrm{0}} \right)=\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{C}_{\mathrm{n}} ^{\mathrm{k}} \mathrm{f}^{\left(\mathrm{k}\right)} \left(\mathrm{x}_{\mathrm{0}} \right)\mathrm{g}^{\left(\mathrm{n}−\mathrm{k}\right)} \left(\mathrm{x}_{\mathrm{0}} \right) \\ $$…

Soient-a-et-b-deux-re-els-Pour-tout-n-N-on-pose-u-n-n-a-n-1-b-n-2-1-Ve-rifier-que-la-suite-u-n-tend-vers-0-si-et-seulement-si-a-b-1-2-De-

Question Number 173795 by Ar Brandon last updated on 18/Jul/22 $$\:\:\:\:\mathrm{Soient}\:{a}\:\mathrm{et}\:{b}\:\mathrm{deux}\:\mathrm{r}\acute {\mathrm{e}els}.\:\mathrm{Pour}\:\mathrm{tout}\:{n}\:\in\:\mathbb{N}\:\mathrm{on}\:\mathrm{pose} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{u}_{{n}} =\sqrt{{n}}+{a}\sqrt{{n}+\mathrm{1}}+{b}\sqrt{{n}+\mathrm{2}}. \\ $$$$\:\:\mathrm{1}.\:\:\mathrm{V}\acute {\mathrm{e}rifier}\:\mathrm{que}\:\mathrm{la}\:\mathrm{suite}\:\left({u}_{{n}} \right)\:\mathrm{tend}\:\mathrm{vers}\:\mathrm{0}\:\mathrm{si}\:\mathrm{et}\:\mathrm{seulement}\:\mathrm{si}\:{a}+{b}=−\mathrm{1}. \\ $$$$\:\:\mathrm{2}.\:\:\mathrm{D}\acute {\mathrm{e}terminer}\:{a}\:\mathrm{et}\:{b}\:\mathrm{pour}\:\mathrm{que}\:\mathrm{la}\:\mathrm{s}\acute {\mathrm{e}rie}\:\Sigma{u}_{{n}} \:\mathrm{soit}\:\mathrm{convergente}.\:\: \\…

Question-42713

Question Number 42713 by Rio Michael last updated on 01/Sep/18 Commented by Rio Michael last updated on 01/Sep/18 $${find}\:{the}\:{Area}\:{bounded}\:{by}\:{the}\:{curve}\:{y}=\:{x}^{\mathrm{2}} ,{the}\:{x}−{axis}\:{and}\: \\ $$$${the}\:{line}\:{x}=\mathrm{2}. \\ $$ Answered…

BeMath-lim-n-n-ln-a-n-n-b-

Question Number 108228 by bemath last updated on 15/Aug/20 $$\:\:\frac{\curlyvee\mathcal{B}{e}\mathcal{M}{ath}\curlyvee}{\pitchfork} \\ $$$$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{n}+\mathrm{ln}\:{a}}{{n}}\right)^{\frac{{n}}{{b}}} ?\: \\ $$ Answered by Dwaipayan Shikari last updated on 15/Aug/20 $$\underset{{n}\rightarrow\infty}…

JS-lim-x-pi-6-2-3-cos-x-sin-x-6x-pi-2-

Question Number 108217 by john santu last updated on 15/Aug/20 $$\:\:\:\:\frac{\heartsuit{JS}\heartsuit}{\leqslant°\equiv°\leqslant} \\ $$$$\:\underset{{x}\rightarrow\pi/\mathrm{6}} {\mathrm{lim}}\frac{\mathrm{2}−\sqrt{\mathrm{3}}\:\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}{\left(\mathrm{6}{x}−\pi\right)^{\mathrm{2}} }\:?\: \\ $$ Commented by john santu last updated on 15/Aug/20…

Evaluate-lim-x-0-x-1-x-x-1-x-2-x-x-1-1-

Question Number 173729 by a.lgnaoui last updated on 17/Jul/22 $${Evaluate} \\ $$$${lim}_{{x}\rightarrow\mathrm{0}} \frac{{x}−\frac{\mathrm{1}}{\:\sqrt{{x}}−{x}}+\mathrm{1}}{{x}^{\mathrm{2}} +\frac{\sqrt{{x}}}{\:\sqrt{{x}}−\mathrm{1}}−\mathrm{1}} \\ $$ Answered by blackmamba last updated on 17/Jul/22 $$\:\:{L}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{{x}−\frac{\mathrm{1}}{\:\sqrt{{x}}−{x}}\:−\mathrm{1}}{{x}^{\mathrm{2}}…