Question Number 184828 by ajfour last updated on 12/Jan/23 $${Find}\:{x}\:{in}\:{terms}\:{of}\:\:\:{c}\:\:\forall\:\mathrm{0}<{c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$$$\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{36}{x}−\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:=\left\{\mathrm{4}\left({x}^{\mathrm{3}} −{x}−{c}\right)+\mathrm{9}\left(\mathrm{7}{x}^{\mathrm{2}} +\mathrm{1}\right)\right\}^{\mathrm{2}} \\ $$ Commented by Frix last updated…
Question Number 184823 by mnjuly1970 last updated on 12/Jan/23 $$ \\ $$$$\:\:\:\mathrm{Lim}_{\:{x}\rightarrow\:\mathrm{0}^{\:+} } \:\:\frac{\:\:\mathrm{1}−\:\:\mathrm{cos}\:\left(\:\mathrm{1}−\:\mathrm{cos}\left(\sqrt{{x}}\:\right)\right)}{{x}^{\:\mathrm{4}} } \\ $$ Answered by cortano1 last updated on 12/Jan/23 $$=\:\underset{{x}\rightarrow\mathrm{0}^{+}…
Question Number 53732 by ajfour last updated on 25/Jan/19 $${f}\left({x}\right)=\frac{\left({x}+{a}\right)\left({x}+{b}\right)}{\left({x}−{a}\right)\left({x}−{b}\right)} \\ $$$${Find}\:{minimum}\:{and}\:{maximum}. \\ $$ Commented by mr W last updated on 25/Jan/19 $${at}\:{x}={a}\:{and}\:{x}={b}:\:{f}\left({x}\right)\rightarrow\pm\infty \\ $$…
Question Number 53709 by pieroo last updated on 25/Jan/19 $$\mathrm{A}\:\mathrm{supermarket}\:\mathrm{pays}\:\mathrm{its}\:\mathrm{sales}\:\mathrm{personnel} \\ $$$$\mathrm{on}\:\mathrm{a}\:\mathrm{weekly}\:\mathrm{basis}.\:\mathrm{At}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{each}\:\mathrm{week}, \\ $$$$\mathrm{each}\:\mathrm{sales}\:\mathrm{person}\:\mathrm{receives}\:\mathrm{a}\:\mathrm{basic}\: \\ $$$$\mathrm{weekly}\:\mathrm{wage}\:\mathrm{plus}\:\mathrm{bonus},\:\mathrm{which}\:\mathrm{varies} \\ $$$$\mathrm{directly}\:\mathrm{as}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{complete} \\ $$$$\mathrm{weeks}\:\mathrm{that}\:\mathrm{particular}\:\mathrm{person}\:\mathrm{has}\: \\ $$$$\mathrm{worked}\:\mathrm{in}\:\mathrm{the}\:\mathrm{shop}.\:\mathrm{At}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{her} \\ $$$$\mathrm{fourth}\:\mathrm{week}\:\mathrm{a}\:\mathrm{sales}\:\mathrm{girl}\:\mathrm{received}\:\mathrm{a}\:\mathrm{pay} \\…
Question Number 184757 by Shrinava last updated on 11/Jan/23 $$\mathrm{Which}\:\mathrm{function}\:\mathrm{has}\:\mathrm{a}\:\mathrm{crisis}\:\mathrm{point}? \\ $$$$\left.\mathrm{a}\right)\mathrm{y}=\mathrm{x}^{\mathrm{3}} +\mathrm{2x}+\mathrm{6} \\ $$$$\left.\mathrm{b}\right)\mathrm{y}=\sqrt[{\mathrm{4}}]{\mathrm{x}} \\ $$$$\left.\mathrm{c}\right)\mathrm{y}=\frac{\mathrm{15}}{\mathrm{x}} \\ $$$$\left.\mathrm{d}\right)\mathrm{y}=\mathrm{e}^{\boldsymbol{\mathrm{x}}} \\ $$$$\left.\mathrm{e}\right)\mathrm{y}=\sqrt[{\mathrm{3}}]{\mathrm{x}} \\ $$ Commented by…
Question Number 184753 by cortano1 last updated on 11/Jan/23 Answered by qaz last updated on 11/Jan/23 $$\underset{{r}\rightarrow\infty} {{lim}}\frac{{r}^{{c}} \int_{\mathrm{0}} ^{\pi/\mathrm{2}} {x}^{{r}} \mathrm{sin}\:{xdx}}{\int_{\mathrm{0}} ^{\pi/\mathrm{2}} {x}^{{r}} \mathrm{cos}\:{xdx}}=\underset{{r}\rightarrow\infty}…
Question Number 119204 by J2 last updated on 22/Oct/20 $$\mathrm{40}−\mathrm{misolning}\:\:\:\mathrm{yechimi}: \\ $$$$\mathrm{y}=\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{3}}+\mathrm{2x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{7} \\ $$$$\mathrm{Kritik}\:\mathrm{nuqtalarini}\:\mathrm{topish}\:\mathrm{uchun}:\: \\ $$$$\mathrm{1}.\:\mathrm{Funksiyadan}\:\mathrm{hosila}\:\mathrm{olamiz} \\ $$$$\mathrm{2}.\:\mathrm{Funksiya}\:\mathrm{hosilasini}\:\mathrm{nolga}\:\mathrm{tenglab},\: \\ $$$$\mathrm{tenglamani}\:\mathrm{yechamiz}. \\ $$$$\mathrm{y}'=\mathrm{x}^{\mathrm{2}} +\mathrm{4x}−\mathrm{5}=\mathrm{0}\:\:\:\Rightarrow\:\:\:\mathrm{x}_{\mathrm{1}}…
Question Number 184738 by mnjuly1970 last updated on 11/Jan/23 $$ \\ $$$$\alpha\:\:,\:\beta\:\:{are}\:{roots}\:{of}\:\:,\:{x}^{\:\mathrm{2}} −{x}−\mathrm{1}=\mathrm{0} \\ $$$$\left(\:\:\alpha\:>\:\beta\:\right)\:{and}\:,\:\:{t}_{\:{n}} =\:\frac{\alpha^{\:{n}} −\:\beta^{\:{n}} }{\alpha−\beta} \\ $$$$\:\left(\:{n}\:\in\:\mathbb{N}\:\right),\:{if}\:,\:{b}_{\mathrm{1}} =\mathrm{1}\:,\:{b}_{\:{n}} =\:{t}_{\:{n}−\mathrm{1}} +{t}_{\:{n}−\mathrm{2}} \\ $$$$\:\:\:\left(\:{n}\:\geqslant\mathrm{2}\:\right)\:{find}\:{the}\:{value}\:{of}…
Question Number 184739 by SLVR last updated on 11/Jan/23 $${Number}\:{of}\:{linear}\:{functions}\: \\ $$$${be}\:{defined}\:{f}:\left[−\mathrm{1},\:\mathrm{1}\right]\rightarrow\left[\mathrm{0},\mathrm{2}\right]\:{is} \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left.\:\:\:\:{b}\right)\mathrm{2}\:\:\:\:{c}\right)\mathrm{3}\:\:\:{d}\right)\mathrm{4} \\ $$ Commented by SLVR last updated on 11/Jan/23 $${kindly}\:{help}\:{me}..{answer}\:{says} \\…
Question Number 184728 by mnjuly1970 last updated on 11/Jan/23 $$ \\ $$$$\:\:\:\:\:\:{x}^{\:\mathrm{2}} −\:\mathrm{3}{x}\:+\mathrm{1}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\alpha\:,\:\beta\:{are}\:{roots}\:: \\ $$$$\:\:\:\left(\:\alpha^{\:\mathrm{3}} \:+\frac{\mathrm{1}}{\beta}\:\right)^{\:\mathrm{3}} \:+\:\left(\:\beta^{\:^{\:\mathrm{3}} } \:+\frac{\mathrm{1}}{\alpha}\:\right)^{\:\mathrm{3}} =\:? \\ $$$$ \\…