Question Number 98880 by Ar Brandon last updated on 16/Jun/20 $$\mathcal{G}\mathrm{iven}\:\mathrm{the}\:\mathrm{sequence}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}^{\ast} } \:\mathrm{defined}\:\mathrm{by}\:\begin{cases}{\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{n}} }\:\mathrm{if}\:\mathrm{n}\equiv\mathrm{0mod}\left(\mathrm{3}\right)}\\{\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{n}} }+\mathrm{1}\:\:\:\mathrm{if}\:\mathrm{n}\equiv\mathrm{1mod}\left(\mathrm{3}\right)}\\{\frac{\mathrm{u}_{\mathrm{n}−\mathrm{1}} +\mathrm{u}_{\mathrm{n}+\mathrm{2}} }{\mathrm{2}}\:\mathrm{if}\:\mathrm{n}\equiv\mathrm{2mod}\left(\mathrm{3}\right)}\end{cases} \\ $$$$\mathrm{a}\backslash\mathcal{D}\mathrm{etermine}\:\mathrm{the}\:\mathrm{first}−\mathrm{8}^{\mathrm{th}} \:\mathrm{terms}\:\mathrm{of}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}^{\ast} } \\ $$$$\mathrm{b}\backslash\mathcal{S}\mathrm{how}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sequences}\:\left(\mathrm{v}_{\mathrm{n}}…
Question Number 98858 by M±th+et+s last updated on 16/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}…….}}}} \\ $$$$ \\ $$ Commented by Tinku Tara last updated on 17/Jun/20 $$\mathrm{Hi}\:\mathrm{David} \\…
Question Number 33313 by abdo imad last updated on 14/Apr/18 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\frac{{ln}\left(\mathrm{1}+{sinx}\right)\:−{sin}\left({ln}\left(\mathrm{1}+{x}\right)\right)}{{x}^{\mathrm{2}} } \\ $$ Commented by abdo imad last updated on 17/Apr/18 $${let}\:{put}\:{u}\left({x}\right)={ln}\left(\mathrm{1}+{sinx}\right)\:−{sin}\left({ln}\left(\mathrm{1}+{x}\right)\right){and}\:{v}\left({x}\right)={x}^{\mathrm{2}} \\…
Question Number 33312 by abdo imad last updated on 14/Apr/18 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{e}^{−\mathrm{3}{x}^{\mathrm{2}} } \:−\mathrm{1}}{{x}^{\mathrm{2}} }\:. \\ $$ Answered by Joel578 last updated on 14/Apr/18 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 98833 by john santu last updated on 16/Jun/20 Commented by bobhans last updated on 16/Jun/20 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{3}^{\mathrm{n}} \:\left(\mathrm{1}+\left(\frac{\mathrm{1}}{\mathrm{6}^{\mathrm{n}} }\right)\right)^{\frac{\mathrm{1}}{\mathrm{n}}} \right)\:=\:\mathrm{3}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{6}^{\mathrm{n}} }\right)^{\frac{\mathrm{1}}{\mathrm{n}}} \\…
Question Number 164364 by Zaynal last updated on 16/Jan/22 $$\boldsymbol{{Lim}}_{\boldsymbol{{x}}\rightarrow\infty} \:\left(\boldsymbol{{e}}^{\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)} \right) \\ $$$$\left\{\boldsymbol{{Z}}.\boldsymbol{\mathrm{A}}\right\} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 98823 by john santu last updated on 16/Jun/20 Commented by bramlex last updated on 16/Jun/20 $${L}'{Hopital}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:{x}+{x}\mathrm{cos}\:{x}}{\mathrm{3}{x}^{\mathrm{2}} }\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{cos}\:{x}+\mathrm{cos}\:{x}−{x}\mathrm{sin}\:{x}}{\mathrm{6}{x}} \\ $$$$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 98788 by Ar Brandon last updated on 16/Jun/20 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{n}}\left[\:\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{2}\right)…\left(\mathrm{n}+\mathrm{n}\right)_{} ^{} \right]^{\frac{\mathrm{1}}{\mathrm{n}}} \\ $$ Answered by Ar Brandon last updated on 16/Jun/20 Answered…
Question Number 98773 by john santu last updated on 16/Jun/20 $$\mathrm{if}\:\mathrm{x}\:\mathrm{is}\:\mathrm{a}\:\mathrm{selected}\:\mathrm{number}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{from}\:\mathrm{20}−\mathrm{99},\:\mathrm{then}\:\mathrm{what} \\ $$$$\mathrm{is}\:\mathrm{probalility}\:\mathrm{x}^{\mathrm{3}} −\mathrm{x}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by} \\ $$$$\mathrm{12}?\: \\ $$ Answered by mr W last…
Question Number 98768 by bemath last updated on 16/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}+\mathrm{1}}\:\mathrm{sin}\:\mathrm{x}+\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)−\mathrm{x}}{\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }−\mathrm{1}} \\ $$ Answered by john santu last updated on 16/Jun/20 Commented by…