Question Number 145165 by mathmax by abdo last updated on 02/Jul/21 $$\mathrm{calculate}\:\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \mathrm{arctan}\left(\frac{\mathrm{2n}+\mathrm{1}}{\mathrm{n}^{\mathrm{4}} \:+\mathrm{2n}^{\mathrm{3}} \:+\mathrm{n}^{\mathrm{2}} \:+\mathrm{1}}\right) \\ $$ Answered by mnjuly1970 last updated on…
Question Number 145119 by imjagoll last updated on 02/Jul/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{5}^{\mathrm{log}\:_{\frac{\mathrm{5}}{\mathrm{3}}} \left(\mathrm{5}\right)} }{\mathrm{3}^{\mathrm{log}\:_{\frac{\mathrm{5}}{\mathrm{3}}} \left(\mathrm{3}\right)} }\:=?\: \\ $$ Answered by Rasheed.Sindhi last updated on 03/Jul/21 $$\:\frac{\mathrm{5}^{\mathrm{log}\:_{\frac{\mathrm{5}}{\mathrm{3}}} \left(\mathrm{5}\right)}…
Question Number 145000 by imjagoll last updated on 01/Jul/21 $$\mathrm{If}\:\mathrm{F}\left(\mathrm{x}+\mathrm{1}\right)=\mathrm{F}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{x}^{\mathrm{2}} \\ $$$$\mathrm{then}\:\mathrm{F}^{−\mathrm{1}} \left(\mathrm{x}\right)=? \\ $$ Commented by prakash jain last updated on 01/Jul/21 $${f}\left({x}+\mathrm{1}\right)={x}^{\mathrm{2}} \Rightarrow{f}\left({x}\right)=\left({x}−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 79419 by jagoll last updated on 25/Jan/20 $$\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…