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Author: Tinku Tara

Know-x-y-z-R-such-that-2x-4y-7z-2xyz-Find-Min-x-y-z-

Question Number 194257 by tri26112004 last updated on 01/Jul/23 $${Know}\:{x},{y},{z}\:\in\:{R}^{+} \:{such}\:{that}: \\ $$$$\mathrm{2}{x}\:+\:\mathrm{4}{y}\:+\:\mathrm{7}{z}\:=\:\mathrm{2}{xyz} \\ $$$${Find}\:{Min}\left({x}+{y}+{z}\right)¿ \\ $$ Commented by Frix last updated on 01/Jul/23 $${x}=\mathrm{3}\wedge{y}=\frac{\mathrm{5}}{\mathrm{2}}\wedge{z}=\mathrm{2}\:\Rightarrow\mathrm{answer}\:\mathrm{is}\:\frac{\mathrm{15}}{\mathrm{2}}…

lim-x-0-1-tan-x-1-tan-x-1-x-

Question Number 194256 by horsebrand11 last updated on 01/Jul/23 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{1}+\mathrm{tan}\:\mathrm{x}}{\mathrm{1}−\mathrm{tan}\:\mathrm{x}}\:−\mathrm{1}}{\mathrm{x}}\:=? \\ $$ Answered by tri26112004 last updated on 01/Jul/23 $$=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}{tan}\:{x}}{{x}\left(\mathrm{1}−{tan}\:{x}\right)} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{tan}\:{x}}{{x}}\:.\:\underset{{x}\rightarrow\mathrm{0}}…

Question-194128

Question Number 194128 by tri26112004 last updated on 28/Jun/23 Answered by MM42 last updated on 28/Jun/23 $$\left.\:\:{a}\right)\:\:\:\:\underset{{n}=\mathrm{2023}} {\overset{\infty} {\sum}}\:\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)^{{n}} =\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)^{{n}} −\underset{{n}=\mathrm{0}} {\overset{\mathrm{2022}} {\sum}}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)^{{n}}…

Question-194127

Question Number 194127 by Rupesh123 last updated on 28/Jun/23 Answered by MM42 last updated on 28/Jun/23 $${AC}={CE}\Rightarrow<{CAE}=\mathrm{45}\Rightarrow{BH}={AH} \\ $$$$\frac{{BH}}{\mathrm{8}}=\frac{{HF}}{\mathrm{6}}\Rightarrow\mathrm{3}{BH}=\mathrm{4}\left(\mathrm{6}−{BH}\right) \\ $$$$\Rightarrow{BH}=\frac{\mathrm{24}}{\mathrm{7}}\Rightarrow{S}=\frac{\mathrm{72}}{\mathrm{7}}\: \\ $$$$ \\ $$…

find-the-value-of-a-for-which-the-limit-lim-x-0-sin-ax-tan-1-x-x-x-3-x-4-is-finite-and-then-evaluate-the-limit-

Question Number 194250 by horsebrand11 last updated on 01/Jul/23 $$\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{limit} \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{ax}\right)−\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)−\mathrm{x}}{\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{4}} }\:\mathrm{is}\:\mathrm{finite}\: \\ $$$$\:\mathrm{and}\:\mathrm{then}\:\mathrm{evaluate}\:\mathrm{the}\:\mathrm{limit}\: \\ $$ Answered by qaz last updated…