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Find-lim-x-0-x-0-x-pi-2-cot-pix-sin-pix-

Question Number 191359 by amin96 last updated on 23/Apr/23 $$\boldsymbol{\mathrm{Find}}\:\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\boldsymbol{\Gamma}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\psi}^{\left(\mathrm{0}\right)} \left(\boldsymbol{\mathrm{x}}\right)+\pi^{\mathrm{2}} \frac{\boldsymbol{\mathrm{cot}}\left(\pi\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{sin}}\left(\pi\boldsymbol{\mathrm{x}}\right)}\right)=? \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…

v2-240-You-can-write-plain-text-using-your-phones-keyboard-choose-insert-plain-text-from-side-bar-Plain-text-can-be-written-in-any-language-An-additional-function-of-loading-

Question Number 125821 by Tinku Tara last updated on 14/Dec/20 $${v}\mathrm{2}.\mathrm{240}\: \\ $$$$\bullet\:\mathrm{You}\:\mathrm{can}\:\mathrm{write}\:\mathrm{plain}\:\mathrm{text}\:\mathrm{using} \\ $$$$\:\:\:\:\mathrm{your}\:\mathrm{phones}\:\mathrm{keyboard}. \\ $$$$\:\:\:\:\mathrm{choose}\:\mathrm{insert}\:\mathrm{plain}\:\mathrm{text}\:\mathrm{from} \\ $$$$\:\:\:\:\mathrm{side}\:\mathrm{bar}.\:\mathrm{Plain}\:\mathrm{text}\:\mathrm{can}\:\mathrm{be} \\ $$$$\:\:\:\:\mathrm{written}\:\mathrm{in}\:\mathrm{any}\:\mathrm{language}. \\ $$$$\bullet\:\mathrm{An}\:\mathrm{additional}\:\mathrm{function}\:\mathrm{of}\:\mathrm{loading} \\ $$$$\:\:\:\:\mathrm{a}\:\mathrm{preview}\:\mathrm{image}\:\mathrm{is}\:\mathrm{available}\:\mathrm{in}…

Let-f-1-5-R-be-defined-by-f-x-6-x-1-Show-that-f-has-a-unique-fixed-point-and-find-it-

Question Number 125814 by Tanuidesire last updated on 14/Dec/20 $${Let}\:{f}:\left[\mathrm{1},\mathrm{5}\right]\rightarrow\mathbb{R}\:{be}\:{defined}\:{by}\:{f}\left({x}\right)=\frac{\mathrm{6}}{{x}+\mathrm{1}}.\:{Show}\:{that}\:{f}\:{has}\:{a}\:{unique}\:{fixed}\:{point}\:{and}\:{find}\:{it}. \\ $$ Answered by Olaf last updated on 14/Dec/20 $${f}\:\mathrm{strictly}\:\mathrm{decreases}\:\mathrm{and}\:: \\ $$$${f}\left(\mathrm{1}\right)\:=\:\frac{\mathrm{6}}{\mathrm{1}+\mathrm{1}}\:=\:\mathrm{3} \\ $$$${f}\left(\mathrm{5}\right)\:=\:\frac{\mathrm{6}}{\mathrm{5}+\mathrm{1}}\:=\:\mathrm{1} \\…

prove-that-the-function-f-x-1-e-x-2-2x-has-a-root-in-the-open-interval-0-1-recall-that-e-2-7-

Question Number 125815 by Tanuidesire last updated on 14/Dec/20 $${prove}\:{that}\:{the}\:{function}\:{f}\left({x}\right)=\frac{\mathrm{1}}{{e}^{{x}} −\mathrm{2}}−\mathrm{2}{x},\:{has}\:{a}\:{root}\:{in}\:{the}\:{open}\:{interval}\:\left(\mathrm{0},\mathrm{1}\right).\:{recall}\:{that}\:{e}\approx\mathrm{2}.\mathrm{7} \\ $$ Answered by physicstutes last updated on 14/Dec/20 $${f}\:\left({x}\right)\:=\:\frac{\mathrm{1}}{{e}^{{x}} −\mathrm{2}}−\mathrm{2}{x} \\ $$$${f}\left(\mathrm{0}\right)\:=\:\frac{\mathrm{1}}{−\mathrm{1}}−\mathrm{0}\:=\:−\mathrm{1} \\…

if-sin-x-3-cos-x-1-2-3-sin-4x-cos-4x-

Question Number 191344 by mnjuly1970 last updated on 23/Apr/23 $$ \\ $$$$\:\:\:\:\:\:\mathrm{if}\:\:\:{sin}\left({x}\right)\:+\:\sqrt{\mathrm{3}}\:{cos}\:\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\Rightarrow\sqrt{\mathrm{3}}\:\:{sin}\left(\mathrm{4}{x}\:\right)\:−\:\:{cos}\:\left(\mathrm{4}{x}\:\right)=\:? \\ $$$$ \\ $$ Answered by mehdee42 last updated on 23/Apr/23…

solve-in-R-1-x-2-x-3-x-1-

Question Number 191343 by mnjuly1970 last updated on 23/Apr/23 $$ \\ $$$$\:\:\:\:\:\:\mathrm{solve}\:\:{in}\:\:\mathbb{R} \\ $$$$ \\ $$$$\:\:\:\:\:\:\lfloor\:\frac{\mathrm{1}}{{x}}\:\rfloor\:+\:\lfloor\:\frac{\mathrm{2}}{{x}}\:\rfloor\:+\:\lfloor\:\frac{\mathrm{3}}{{x}}\:\rfloor\:=\:\mathrm{1} \\ $$$$ \\ $$ Answered by mr W last…