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if-y-sin-1-2x-1-x-2-where-x-1-2-1-2-then-find-dy-dx-

Question Number 190660 by vishal1234 last updated on 08/Apr/23 $${if}\:{y}\:=\:{sin}^{−\mathrm{1}} \left(\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)\:{where}\:{x}\in\left[−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}},\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right],\:{then}\:{find}\:\frac{{dy}}{{dx}}. \\ $$ Answered by BaliramKumar last updated on 08/Apr/23 $$\mathrm{let},\:{x}\:=\:{sin}\theta\:\Rightarrow\:\theta\:=\:{sin}^{−\mathrm{1}} {x} \\ $$$${y}\:=\:{sin}^{−\mathrm{1}}…

Question-190667

Question Number 190667 by 073 last updated on 08/Apr/23 Answered by manxsol last updated on 08/Apr/23 $${ABABAB}\:\mid\:{AB} \\ $$$$\underset{−} {{AB}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{10101} \\ $$$$\:\:\:\:\:\mathrm{0}{A}\boldsymbol{{B}} \\ $$$$\:\:\:\:\:\:\:\:\underset{−} {{AB}}…

The-points-A-B-and-C-have-position-vectors-i-j-5i-3j-and-11i-6j-respectively-Show-that-A-B-and-C-are-collinear-

Question Number 190639 by otchereabdullai last updated on 07/Apr/23 $$\:{The}\:{points}\:{A},\:{B}\:{and}\:{C}\:{have}\:{position} \\ $$$$\:{vectors}\:{i}−{j}\:,\:\mathrm{5}{i}−\mathrm{3}{j}\:{and}\:\mathrm{11}{i}−\mathrm{6}{j}\: \\ $$$${respectively}\:.\:{Show}\:{that}\:{A},\:{B}\:{and}\:{C} \\ $$$${are}\:{collinear}. \\ $$ Answered by ajfour last updated on 08/Apr/23…

lim-x-x-2-3x-x-

Question Number 125089 by bounhome last updated on 08/Dec/20 $${lim}_{{x}\rightarrow−\infty} \left(\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}}−{x}\right)=? \\ $$ Answered by Bird last updated on 08/Dec/20 $${f}\left({x}\right)=\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}}−{x}\:\Rightarrow \\ $$$${f}\left({x}\right)=\mid{x}\mid\sqrt{\mathrm{1}+\frac{\mathrm{3}}{{x}}}−{x}…

How-many-positive-integers-less-than-200-have-exaxtly-6-positive-factors-

Question Number 125080 by ZiYangLee last updated on 08/Dec/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{less}\:\mathrm{than} \\ $$$$\mathrm{200}\:\mathrm{have}\:\mathrm{exaxtly}\:\mathrm{6}\:\mathrm{positive}\:\mathrm{factors}? \\ $$ Answered by mr W last updated on 08/Dec/20 $${say}\:{such}\:{a}\:{number}\:{is} \\ $$$${n}={p}^{{a}}…

Question-59516

Question Number 59516 by naka3546 last updated on 11/May/19 Answered by tanmay last updated on 11/May/19 $$\bigtriangleup=\frac{\mathrm{1}}{\mathrm{2}}{r}\left({a}+{b}+{c}\right)=\sqrt{{s}\left({s}−{a}\right)\left({s}−{b}\right)\left({s}−{c}\right)\:} \\ $$$${s}=\frac{{a}+{b}+{c}}{\mathrm{2}}=\frac{\mathrm{2}{x}+\mathrm{2}{y}+\mathrm{2}{z}}{\mathrm{2}}={x}+{y}+{z} \\ $$$$ \\ $$$$\frac{{x}+{y}+{z}}{\mathrm{3}}\geqslant\left({xyz}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$${x}+{y}+{z}\geqslant\mathrm{3}\left({xyz}\right)^{\frac{\mathrm{1}}{\mathrm{3}}}…

Question-190583

Question Number 190583 by 073 last updated on 06/Apr/23 Answered by mr W last updated on 06/Apr/23 $${f}\left(\mathrm{2}\right)=\mathrm{2}\sqrt{\mathrm{3}} \\ $$$${f}'\left(\mathrm{2}\right)=\mathrm{tan}\:\mathrm{60}°=\sqrt{\mathrm{3}} \\ $$$${g}'\left({x}\right)=\mathrm{2}{xf}\left({x}\right)+{x}^{\mathrm{2}} {f}'\left({x}\right) \\ $$$${g}'\left(\mathrm{2}\right)=\mathrm{2}×\mathrm{2}{f}\left(\mathrm{2}\right)+\mathrm{2}^{\mathrm{2}}…