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Question-137112

Question Number 137112 by Algoritm last updated on 29/Mar/21 Answered by Ñï= last updated on 03/Apr/21 $$\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{3}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\mathrm{9}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{4}}{\mathrm{23}}\right)+… \\ $$$$={arg}\left(\mathrm{3}+{i}\right)+{arg}\left(\mathrm{9}+\mathrm{2}{i}\right)+{arg}\left(\mathrm{23}+\mathrm{4}{i}\right)+… \\ $$$$={arg}\left[\left(\mathrm{3}+{i}\right)\left(\mathrm{9}+\mathrm{2}{i}\right)\left(\mathrm{23}+\mathrm{4}{i}\right)\centerdot…\right] \\…

Question-137069

Question Number 137069 by 0731619177 last updated on 29/Mar/21 Answered by Ñï= last updated on 29/Mar/21 $$\left(\mathrm{1}\right){y}_{{p}} =\frac{\mathrm{1}}{{D}^{\mathrm{2}} +\mathrm{2}{D}+\mathrm{5}}\left(\mathrm{6sin}\:\mathrm{2}{x}+\mathrm{7cos}\:\mathrm{2}{x}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}{D}+\mathrm{1}}\left(\mathrm{6sin}\:\mathrm{2}{x}+\mathrm{7cos}\:\mathrm{2}{x}\right)=\frac{\left(\mathrm{1}+\mathrm{2}{D}\right)}{\mathrm{9}}\left(\mathrm{6sin}\:\mathrm{2}\boldsymbol{{x}}+\mathrm{7cos}\:\mathrm{2}{x}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{9}}\left(\mathrm{31cos}\:\mathrm{2}{x}−\mathrm{22sin}\:\mathrm{2}{x}\right) \\ $$$${y}={e}^{−{x}}…

On-this-same-day-last-year-I-made-my-first-on-this-forum-Q86484-and-I-was-very-astonished-by-the-answers-which-I-received-I-underestimated-the-place-at-first-before-getting-to-know-it-better-A

Question Number 137056 by Ar Brandon last updated on 29/Mar/21 $$\:\:\:\:\mathrm{On}\:\mathrm{this}\:\mathrm{same}\:\mathrm{day}\:\mathrm{last}\:\mathrm{year}\:\mathrm{I}\:\mathrm{made}\:\mathrm{my}\:\mathrm{first}\:\mathrm{on}\:\mathrm{this}\:\mathrm{forum}\:\left(\mathrm{Q86484}\right) \\ $$$$\mathrm{and}\:\mathrm{I}\:\mathrm{was}\:\mathrm{very}\:\mathrm{astonished}\:\mathrm{by}\:\mathrm{the}\:\mathrm{answers}\:\mathrm{which}\:\mathrm{I}\:\mathrm{received}. \\ $$$$\mathrm{I}\:\mathrm{underestimated}\:\mathrm{the}\:\mathrm{place}\:\mathrm{at}\:\mathrm{first}\:\mathrm{before}\:\mathrm{getting}\:\mathrm{to}\:\mathrm{know}\:\mathrm{it} \\ $$$$\mathrm{better}.\:\mathrm{And}\:\mathrm{I}\:\mathrm{realised}\:\mathrm{I}\:\mathrm{knew}\:\mathrm{nothing}.\: \\ $$$$\:\:\:\:\mathrm{I}'\mathrm{m}\:\mathrm{grateful}\:\mathrm{with}\:\mathrm{all}\:\mathrm{the}\:\mathrm{teachings}\:\mathrm{which}\:\mathrm{I}'\mathrm{ve}\:\mathrm{acquired}\:\mathrm{from}\: \\ $$$$\mathrm{you}\:\mathrm{all}.\:\mathrm{You}\:\mathrm{guys}\:\mathrm{are}\:\mathrm{just}\:\mathrm{so}\:\mathrm{amazing}.\:\mathrm{Thank}\:\mathrm{you}\:\mathrm{once}\:\mathrm{more}. \\ $$$$\mathrm{Special}\:\mathrm{thanks}\:\mathrm{to}\:\mathrm{you}\:\mathrm{too}\:\mathrm{Mr}\:\mathrm{Tinku}-\mathrm{Tara}.\: \\ $$😉…