Question Number 204469 by DeArtist last updated on 18/Feb/24 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)\:=\:\begin{cases}{\mathrm{2},\:\mathrm{0}<\:{x}\:<\mathrm{2}}\\{−\mathrm{2},\:−\mathrm{2}\:<{x}\:<\:\mathrm{0}}\end{cases} \\ $$$$\mathrm{of}\:\mathrm{period}\:\mathrm{4} \\ $$$$\left(\mathrm{a}\right)\:\:\mathrm{sketch}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:{y}\:=\:{f}\left({x}\right)\:,\:\mathrm{for}\:−\mathrm{6}\:<\:{x}\:<\:\mathrm{6} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{Fourier}\:\mathrm{coefficient}\:{a}_{\mathrm{0}} ,\:{a}_{{n}} ,\:\mathrm{and}\:{b}_{{n}} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{write}\:\mathrm{down}\:\mathrm{the}\:\mathrm{Fourier}\:\mathrm{series}.\: \\ $$$$\left(\mathrm{d}\right)\:\mathrm{hence}\:\mathrm{show}\:\mathrm{that}\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}{n}−\mathrm{1}}\:=\:\frac{\pi}{\mathrm{4}}…
Question Number 204471 by Abdullahrussell last updated on 18/Feb/24 Answered by TonyCWX08 last updated on 18/Feb/24 $$ \\ $$ Answered by MM42 last updated on…
Question Number 204461 by MATHEMATICSAM last updated on 18/Feb/24 $$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$$\left({x}\:−\:\mathrm{12}\right)\left({x}\:−\:\mathrm{13}\right)\:=\:\frac{\mathrm{34}}{\mathrm{33}^{\mathrm{2}} } \\ $$ Answered by TonyCWX08 last updated on 18/Feb/24 $${x}^{\mathrm{2}} −\mathrm{25}{x}+\mathrm{156}\:=\:\frac{\mathrm{34}}{\mathrm{1089}} \\…
Question Number 204480 by EJJDJX last updated on 18/Feb/24 $${x}\:+\:\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{2}.\mathrm{05} \\ $$$${x}\:=\:? \\ $$ Commented by TonyCWX08 last updated on 19/Feb/24 $$ \\ $$$${x}^{\mathrm{2}} +\mathrm{1}=\:\mathrm{2}.\mathrm{05}{x}…
Question Number 204428 by sulaymonnorboyev140 last updated on 17/Feb/24 Commented by AST last updated on 17/Feb/24 $${Q}\mathrm{196938} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 204441 by peter frank last updated on 17/Feb/24 Commented by Frix last updated on 17/Feb/24 $$\mathrm{3}\:\mathrm{circles}\:\mathrm{plus}\:\mathrm{4}\:\mathrm{times}\:\left(\mathrm{6}\:\mathrm{minus}\:\mathrm{4}\:\mathrm{radii}\right)\:\Rightarrow \\ $$$$\mathrm{perimeter}\:=\:\mathrm{6}\pi+\mathrm{8} \\ $$ Commented by peter…
Question Number 204426 by universe last updated on 17/Feb/24 $$\:\:\mathrm{let}\:\mathrm{a}\:,\:\mathrm{b}\:>\mathrm{0}\:\:\mathrm{find}\:\mathrm{all}\:\mathrm{differentiable}\:\mathrm{function} \\ $$$$\:\:\:\mathrm{f}:\left(\mathrm{0},\infty\right)\rightarrow\left(\mathrm{0},\infty\right)\:\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\:\:\:\mathrm{f}'\left(\frac{{a}}{\mathrm{x}}\right)\:\:=\:\:\frac{\mathrm{bx}}{\mathrm{f}\left(\mathrm{x}\right)}\:\:\:\:,\:\:\:\forall\:\mathrm{x}>\mathrm{0} \\ $$ Answered by MrGaster last updated on 03/Feb/25 $$\mathrm{Let}\:{f}\left({x}\right)=\sqrt{{bx}^{\mathrm{2}} +{c}},{c}=\frac{{a}^{\mathrm{2}}…
Question Number 204436 by otchereabdullai@gmail.com last updated on 17/Feb/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 204437 by SANOGO last updated on 17/Feb/24 $$\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} {sin}\left({t}\right){ln}\left({sint}\right){dt} \\ $$ Answered by TonyCWX08 last updated on 18/Feb/24 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}{ln}\left({sin}\left({t}\right)\right){sin}\left({t}\right){dt} \\…
Question Number 204421 by necx122 last updated on 17/Feb/24 $${x}^{\mathrm{3}} +{y}^{\mathrm{3}} \:=\:\mathrm{35} \\ $$$$\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}\:=\frac{\mathrm{5}}{\mathrm{6}} \\ $$$${solve}\:{for}\:{all}\:{possible}\:{values}\:{of}\:{x}\:{and}\:{y} \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last updated…