Question Number 79419 by jagoll last updated on 25/Jan/20 $$\mathrm{given}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}+\mathrm{5}\right)\:\forall\mathrm{x}\in\mathbb{R} \\ $$$$\mathrm{If}\:\int\:_{\mathrm{7}} ^{\mathrm{9}} \:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{t}\:\mathrm{and}\:\int\:_{\mathrm{2}} ^{\mathrm{6}} \:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\:= \\ $$$$\mathrm{t}^{\mathrm{2}} +\mathrm{4t}−\mathrm{3}\:.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{t}. \\ $$ Commented by…
Question Number 13811 by Tinkutara last updated on 23/May/17 $$\mathrm{The}\:\mathrm{domain}\:\mathrm{of}\:{f}\left({x}\right)\:=\:\sqrt{\mathrm{2}\:−\:\mathrm{2}^{{x}} \:−\:\mathrm{2}^{\mathrm{2}{x}} }\:\mathrm{is}? \\ $$ Commented by RasheedSindhi last updated on 24/May/17 $$\mathrm{Sorry},\:\mathrm{wrong}\:\mathrm{process}. \\ $$ Answered…
Question Number 13812 by Tinkutara last updated on 23/May/17 $$\mathrm{The}\:\mathrm{domain}\:\mathrm{of}\:{f}\left({x}\right)\:= \\ $$$$\sqrt{\left(\frac{\mathrm{4}}{\mathrm{3}}\right)^{\mathrm{4}−{x}} −\left(\frac{\mathrm{27}}{\mathrm{64}}\right)^{{x}−\mathrm{5}} };\:\mathrm{is}? \\ $$ Answered by ajfour last updated on 23/May/17 $$\left(\frac{\mathrm{4}}{\mathrm{3}}\right)^{\mathrm{4}−{x}} \geqslant\left(\frac{\mathrm{4}}{\mathrm{3}}\right)^{\mathrm{15}−\mathrm{3}{x}}…
Question Number 13808 by Tinkutara last updated on 23/May/17 $$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{defined}\:\mathrm{over}\:\mathrm{the}\:\mathrm{domain}\:\left[\mathrm{0},\:\mathrm{1}\right] \\ $$$$\mathrm{then}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{function}\:{f}\left(\mathrm{10}^{{x}} \right)\:\mathrm{is}? \\ $$ Answered by ajfour last updated on 23/May/17 $${then}\:{x}\leqslant\mathrm{0}\: \\ $$$$\mathrm{0}\leqslant\mathrm{10}^{{x}}…
Question Number 144781 by imjagoll last updated on 29/Jun/21 Answered by liberty last updated on 29/Jun/21 $$\:\mid\mathrm{PF}_{\mathrm{1}} \mid+\mid\mathrm{PF}_{\mathrm{2}} \mid=\mathrm{2a}\:=\mathrm{6}\:,\:\mathrm{by}\:\mathrm{definition} \\ $$$$\mathrm{of}\:\mathrm{an}\:\mathrm{ellipse}.\:\mathrm{Since}\:\mid\mathrm{PF}_{\mathrm{1}} \mid:\mid\mathrm{PF}_{\mathrm{2}} \mid=\mathrm{2}:\mathrm{1} \\ $$$$\mathrm{we}\:\mathrm{get}\:\begin{cases}{\mid\mathrm{PF}_{\mathrm{1}}…
Question Number 144701 by mathmax by abdo last updated on 28/Jun/21 $$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{cos}\left(\mathrm{n}\theta\right)}{\mathrm{n}^{\mathrm{2}} } \\ $$ Answered by Dwaipayan Shikari last updated on 28/Jun/21…
Question Number 144702 by mathmax by abdo last updated on 28/Jun/21 $$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{log}\left(\mathrm{cosx}\:+\mathrm{2sinx}\right) \\ $$$$\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$$$ \\ $$ Answered by mathmax by abdo last updated…
Question Number 144700 by mathmax by abdo last updated on 28/Jun/21 $$\mathrm{find}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{x}^{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} } \\ $$ Answered by qaz last updated on 28/Jun/21…
Question Number 144699 by mathmax by abdo last updated on 28/Jun/21 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{log}\left(\mathrm{cht}\right) \\ $$$$\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by Olaf_Thorendsen last updated on 28/Jun/21 $${f}\:\mathrm{is}\:\mathrm{not}\:\mathrm{periodic}\:! \\…
Question Number 13598 by Tinkutara last updated on 21/May/17 $$\mathrm{If}\:{g}\left({x}\right)\:=\:{x}^{\mathrm{2}} \:+\:{x}\:−\:\mathrm{2}\:\mathrm{and} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\:{gof}\left({x}\right)\:=\:\mathrm{2}{x}^{\mathrm{2}} \:−\:\mathrm{5}{x}\:+\:\mathrm{2},\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:{f}\left({x}\right)\:=\:\mathrm{2}{x}\:−\:\mathrm{3}. \\ $$ Commented by mrW1 last updated on 21/May/17…