Question Number 155816 by cortano last updated on 05/Oct/21 $$\:\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number}\:\mathrm{formed} \\ $$$$\:\mathrm{by}\:\mathrm{using}\:\mathrm{all}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6} \\ $$$$\:\mathrm{only}\:\mathrm{once}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{25}. \\ $$ Answered by talminator2856791 last updated on 05/Oct/21 $$\:\mathrm{4}!\:=\:\mathrm{24} \\…
Question Number 90281 by jagoll last updated on 22/Apr/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt{\mathrm{x}}}{\left(\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{x}\right)\right)^{\mathrm{2}} }\:=\:? \\ $$ Commented by jagoll last updated on 22/Apr/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{x}}}}{\mathrm{2cos}^{−\mathrm{1}} \left(\mathrm{x}\right).\left(\frac{−\mathrm{1}}{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}}…
Question Number 24744 by NECx last updated on 25/Nov/17 $${If}\:{a}\:{function}\:{f}\:{is}\:{defined}\:{such}\:{that} \\ $$$${f}:\mathbb{R}\rightarrow\mathbb{R}.{If}\: \\ $$$$\:\:\:\:{f}\left({x}\right)=\frac{\mathrm{3}{x}−\mathrm{2}}{{x}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{6}}.{Find}\:{the}\: \\ $$$$\left({i}\right){domain}\:{of}\:{f}\left({x}\right) \\ $$$$\left({ii}\right){range}\:{of}\:{f}\left({x}\right) \\ $$ Answered by ajfour last…
Question Number 155812 by zainaltanjung last updated on 05/Oct/21 $$\mathrm{Use}\:\mathrm{algebraic}\:\mathrm{simplifications}\:\mathrm{to}\:\mathrm{help} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{limits},\:\mathrm{if}\:\mathrm{they}\:\mathrm{exist}. \\ $$$$\left.\mathrm{1}\right).\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{4}}{\mathrm{x}−\mathrm{2}} \\ $$$$\left.\mathrm{2}\right).\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\:\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{x}}{\mathrm{2x}^{\mathrm{2}} +\mathrm{5x}−\mathrm{7}} \\ $$$$\left.\mathrm{3}\right).\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\:\:\frac{\mathrm{3x}^{\mathrm{2}} −\mathrm{13x}−\mathrm{10}}{\mathrm{2x}^{\mathrm{2}}…
Question Number 90279 by mathmax by abdo last updated on 22/Apr/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}\:{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 155809 by zainaltanjung last updated on 05/Oct/21 $$\:\:\mathrm{Given}\:\mathrm{that}\:{f}\circ{g}\:=\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}{x}^{\mathrm{2}} \:−\:{x}\:+\:\mathrm{4}}\:\:\mathrm{and} \\ $$$$\:\:{g}\left({x}\right)\:=\:\frac{{x}}{{x}\:−\:\mathrm{2}},\:\mathrm{find}\:{f}\left({x}\right)\:? \\ $$$$ \\ $$ Answered by PRITHWISH SEN 2 last updated…
Question Number 24739 by Tinkutara last updated on 25/Nov/17 $${A}\:{particle}\:{is}\:{suspended}\:{vertically} \\ $$$${from}\:{point}\:{O}\:{by}\:{ideal}\:{string}\:{of}\:{length} \\ $$$${L}.\:{It}\:{is}\:{given}\:{horizontal}\:{velocity}\:'{v}'. \\ $$$${There}\:{is}\:{vertical}\:{line}\:{AB}\:{at}\:{a}\:{distance} \\ $$$$\frac{{L}}{\mathrm{8}}\:{from}\:{P}.\:{At}\:{some}\:{point},\:{it}\:{leaves} \\ $$$${circular}\:{motion}\:{and}\:{follows}\:{projectile} \\ $$$${motion}.\:{At}\:{the}\:{instant}\:{it}\:{crosses}\:{AB}, \\ $$$${its}\:{velocity}\:{is}\:{horizontal}.\:{Find}\:{u} \\…
Question Number 90272 by student work last updated on 22/Apr/20 Answered by behi83417@gmail.com last updated on 22/Apr/20 $$\mathrm{AO}+\mathrm{OC}=\mathrm{8} \\ $$$$\mathrm{AO}^{\mathrm{2}} +\mathrm{OC}^{\mathrm{2}} =\mathrm{6}^{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{AO}.\mathrm{OC}=\frac{\mathrm{1}}{\mathrm{2}}\left[\left(\mathrm{AO}+\mathrm{OC}\right)^{\mathrm{2}} −\left(\mathrm{AO}^{\mathrm{2}}…
Question Number 155810 by zainaltanjung last updated on 05/Oct/21 $$\mathrm{Verify}\:\mathrm{the}\:\mathrm{identity}\:\mathrm{in}\:\mathrm{Excercise}\:\mathrm{below} \\ $$$$\left.\mathrm{1}\right).\:\mathrm{cos}\:\theta\mathrm{sec}\:\theta=\mathrm{1} \\ $$$$\left.\mathrm{2}\right).\:\left(\mathrm{1}+\mathrm{cos}\:\beta\right)\left(\mathrm{1}−\mathrm{cos}\:\beta\right)=\mathrm{sin}\:^{\mathrm{2}} \beta \\ $$$$\left.\mathrm{3}\right).\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\left(\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}−\mathrm{1}\right)=\mathrm{sin}\:^{\mathrm{2}} \mathrm{x} \\ $$$$\left.\mathrm{4}\right).\:\frac{\mathrm{sin}\:\mathrm{t}}{\mathrm{cosec}\:\mathrm{t}}+\frac{\mathrm{cos}\:\mathrm{t}}{\mathrm{sec}\:\mathrm{t}}=\mathrm{1} \\ $$$$\left.\mathrm{5}\right).\:\frac{\mathrm{cosec}\:^{\mathrm{2}} \theta}{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}}…
Question Number 24733 by chernoaguero@gmail.com last updated on 25/Nov/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{second}\:\mathrm{derivative}\:\mathrm{of} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\sqrt{\mathrm{5x}+\mathrm{9}} \\ $$$$\mathrm{find}\:\mathrm{f}^{''} \\ $$ Commented by chernoaguero@gmail.com last updated on 25/Nov/17 $$\mathrm{Using}\:\mathrm{the}\:\mathrm{first}\:\mathrm{principle}\:\mathrm{method} \\…