Question Number 226901 by mr W last updated on 18/Dec/25 $${if}\:{x}+{y}=\mathrm{2}\:{with}\:{x},\:{y}\:>\mathrm{0},\:{find}\:{the} \\ $$$${minimum}\:{of}\:{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} }. \\ $$ Commented by fantastic2 last updated on 18/Dec/25 $$\mathrm{3}…
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Question Number 226879 by Spillover last updated on 17/Dec/25 Answered by gregori last updated on 18/Dec/25 $$\left({a}\right)\:{f}\:'\left({x}\right)=\:−\mathrm{sin}\:{x}\:.\:{e}^{\mathrm{cos}\:{x}} \: \\ $$$$\:\left({b}\right)\:{f}\:'\left({x}\right)\:=\:\mathrm{3sin}\:^{\mathrm{2}} {x}\:\mathrm{cos}\:{x}\:.{e}^{\mathrm{sin}\:^{\mathrm{3}} {x}} \\ $$$$ \\…
Question Number 226878 by Spillover last updated on 17/Dec/25 Answered by gregori last updated on 18/Dec/25 $$\:=\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{x}}−\sqrt{{x}+{h}}}{\left(\sqrt{{x}+{h}}\:.\sqrt{{x}}\:\right){h}} \\ $$$$\:=\:\frac{\mathrm{1}}{{x}}\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{−{h}}{\left(\sqrt{{x}}+\sqrt{{x}+{h}}\:\right){h}} \\ $$$$\:=\:−\frac{\mathrm{1}}{{x}.\:\mathrm{2}\sqrt{{x}}}\:=\:−\frac{\mathrm{1}}{\mathrm{2}{x}\sqrt{{x}}} \\ $$…
Question Number 226880 by Spillover last updated on 17/Dec/25 Answered by TonyCWX last updated on 18/Dec/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left[\mathrm{2}^{{x}} \right]\mathrm{d}{x} \\ $$$$=\:\int_{\mathrm{0}} ^{\mathrm{1}} \left[{e}^{{x}\mathrm{ln}\left(\mathrm{2}\right)} \right]\mathrm{d}{x}…
Question Number 226882 by hardmath last updated on 17/Dec/25 Answered by breniam last updated on 17/Dec/25 $$=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}}{\:\frac{\sqrt[{{n}}]{\mathrm{2}^{{n}+\mathrm{1}} }−\mathrm{1}}{\:\sqrt[{{n}}]{\mathrm{2}}−\mathrm{1}}}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}\left(\sqrt[{{n}}]{\mathrm{2}}−\mathrm{1}\right)}{\mathrm{2}\sqrt[{{n}}]{\mathrm{2}}−\mathrm{1}} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{2}\sqrt[{{n}}]{\mathrm{2}}−\mathrm{1}\right)=\mathrm{2}−\mathrm{1}=\mathrm{1} \\ $$$$\underset{{x}\rightarrow\infty}…
Question Number 226812 by mr W last updated on 15/Dec/25 $${if}\:\mathrm{28}{x}+\mathrm{30}{y}+\mathrm{31}{z}=\mathrm{360}\:{with}\:{x},\:{y},\:{z} \\ $$$${being}\:{positive}\:{integers},\:{find} \\ $$$${x}+{y}+{z}=? \\ $$ Commented by Ghisom_ last updated on 15/Dec/25 $$\mathrm{12}…
Question Number 226766 by mr W last updated on 13/Dec/25 Answered by mahdipoor last updated on 13/Dec/25 $$\mathrm{if}\:\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{ax}+\mathrm{b}\:\Rightarrow \\ $$$$\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}+\mathrm{1}\:\mathrm{or}\:−\mathrm{2x}−\mathrm{3} \\ $$$$\mathrm{but}\:\mathrm{its}\:\mathrm{only}\:\mathrm{answer}? \\ $$$$\mathrm{all}\:\mathrm{function}\:\mathrm{can}\:\mathrm{show}\:\mathrm{as}\:\mathrm{f}\left(\mathrm{x}\right)=\underset{\mathrm{i}=\mathrm{0}} {\overset{\mathrm{m}}…
Question Number 226743 by MrAjder last updated on 12/Dec/25 $$ \\ $$$${Prove}:\frac{\mathrm{1}}{\mathrm{2}{ne}}<\frac{\mathrm{1}}{{e}}−\left(\mathrm{1}−\frac{\mathrm{1}}{{n}}\right)^{{n}} <\frac{\mathrm{1}}{{ne}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com