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Category: Limits

L-lim-x-0-1-x-2-tan-1-1-x-2-a-2-1-

Question Number 213073 by ajfour last updated on 29/Oct/24 $${L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\mathrm{1}+\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }}−\mathrm{1}\right)\right\} \\ $$ Answered by universe last updated on 29/Oct/24 $${L}\:=\:\underset{{x}\rightarrow\mathrm{0}}…

Notation-Soit-A-une-partie-de-R-On-appelle-indicatrice-de-A-note-e-A-l-application-x-1-si-x-A-0-sinon-1-Pour-k-dans-N-notons-f-k-x-cos-x-2k-Montrer-que-f-

Question Number 212984 by Faetmaaa last updated on 27/Oct/24 $$\underline{\boldsymbol{\mathrm{Notation}}\::}\:\mathrm{Soit}\:{A}\:\mathrm{une}\:\mathrm{partie}\:\mathrm{de}\:\mathbb{R}.\:\mathrm{On}\:\mathrm{appelle}\:{indicatrice}\:{de}\:{A}, \\ $$$$\mathrm{not}\acute {\mathrm{e}e}\:\chi_{{A}} ,\:\mathrm{l}'\mathrm{application}\:{x}\: \:\begin{cases}{\mathrm{1}\:\mathrm{si}\:{x}\:\in\:{A}}\\{\mathrm{0}\:\mathrm{sinon}}\end{cases}. \\ $$$$ \\ $$$$\mathrm{1}.\:\mathrm{Pour}\:{k}\:\mathrm{dans}\:\mathbb{N}^{\ast} \:\mathrm{notons}\:{f}_{{k}} \::\:{x}\: \:\left(\mathrm{cos}\:{x}\right)^{\mathrm{2}{k}} . \\ $$$$\mathrm{Montrer}\:\mathrm{que}\:\left({f}_{{k}}…

Question-212762

Question Number 212762 by universe last updated on 23/Oct/24 Commented by MrGaster last updated on 23/Oct/24 $$\mathrm{Rewrite}\:\mathrm{the}\:\mathrm{integrand}\:\mathrm{function}\:\mathrm{as}: \\ $$$$\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\ldots\left({x}−{n}\right)=\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}!}{x}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\ldots\left({x}−{n}\right) \\ $$$$\mathrm{Computational}\:\mathrm{integral}: \\ $$$$\int_{\mathrm{0}} ^{{n}}…

Question-212745

Question Number 212745 by RoseAli last updated on 22/Oct/24 Answered by mehdee7396 last updated on 22/Oct/24 $${lim}_{{x}\rightarrow\mathrm{0}} \left(\frac{\mathrm{1}+{tanx}}{\mathrm{1}−{tanx}}−\mathrm{1}\right)×\frac{\mathrm{1}}{{sinx}} \\ $$$$={lim}_{{x}\rightarrow\mathrm{0}} \left(\frac{\mathrm{2}{tanx}}{\mathrm{1}−{tanx}}\right)×\frac{\mathrm{1}}{{sinx}} \\ $$$$={lim}_{{x}\rightarrow\mathrm{0}} \left(\frac{\mathrm{2}}{\mathrm{1}−{tanx}}\right)×\frac{\mathrm{1}}{{cosx}}=\mathrm{2} \\…

lim-x-3-e-x-e-3-x-3-

Question Number 212405 by mathlove last updated on 13/Oct/24 $$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\frac{{e}^{{x}} −{e}^{\mathrm{3}} }{{x}−\mathrm{3}}=? \\ $$ Answered by som(math1967) last updated on 13/Oct/24 $$\underset{{x}\rightarrow\mathrm{3}} {\:{lim}}\frac{{e}^{\mathrm{3}} \left({e}^{{x}−\mathrm{3}}…

lim-0-2-e-x-1-2-x-dx-

Question Number 212169 by universe last updated on 04/Oct/24 $$\:\:\:\:\:\:\:\:\:\:\underset{\lambda\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\:\int_{\lambda} ^{\mathrm{2}\lambda} \:\frac{{e}^{\left({x}−\mathrm{1}\right)^{\mathrm{2}} } }{{x}}{dx}\:=\:? \\ $$ Answered by MrGaster last updated on 03/Nov/24…