Question Number 35987 by abdo mathsup 649 cc last updated on 26/May/18 $${let}\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{3}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$ Commented by prof Abdo…
Question Number 35960 by Joel579 last updated on 26/May/18 $$\mathrm{Solve}\:\mathrm{using}\:\mathrm{Residue}\:\mathrm{Theorem} \\ $$$$\mathrm{I}\:=\:\int_{−\infty} ^{+\infty} \:\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} \:+\:\mathrm{16}}\:{dx} \\ $$ Commented by abdo mathsup 649 cc last…
Question Number 101476 by 175 last updated on 02/Jul/20 Answered by Ar Brandon last updated on 03/Jul/20 $$\mathrm{a}\backslash\:\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{f}\left(\mathrm{x}_{\mathrm{r}} \right)\mathrm{dx} \\ $$ Terms of…
Question Number 101474 by 175 last updated on 02/Jul/20 Answered by 1549442205 last updated on 07/Jul/20 $$\left(\boldsymbol{\mathrm{see}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{solution}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{question}}\:\mathrm{101247}\right) \\ $$$$\boldsymbol{\mathrm{we}}\:\boldsymbol{\mathrm{known}}\:\boldsymbol{\mathrm{that}}\:\left[\left(\mathrm{2}+\sqrt{\mathrm{2}}\right)^{\boldsymbol{\mathrm{n}}} \right]=\left(\mathrm{2}+\sqrt{\mathrm{2}}\right)^{\boldsymbol{\mathrm{n}}} +\left(\mathrm{2}−\sqrt{\mathrm{2}}\right)^{\boldsymbol{\mathrm{n}}} −\mathrm{1} \\ $$$$\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{an}}\:\boldsymbol{\mathrm{odd}}\:\boldsymbol{\mathrm{number}}.\boldsymbol{\mathrm{Putting}}\:\boldsymbol{\mathrm{A}}_{\boldsymbol{\mathrm{n}}} =\left(\mathrm{2}+\sqrt{\mathrm{2}}\right)^{\boldsymbol{\mathrm{n}}}…
Question Number 101473 by 175 last updated on 02/Jul/20 Answered by 1549442205 last updated on 03/Jul/20 $$ \\ $$$$\mathrm{We}\:\mathrm{prove}\:\mathrm{by}\:\mathrm{induction}\:\mathrm{method}\:\mathrm{that} \\ $$$$\exists\mathrm{m}\in\boldsymbol{\mathrm{N}}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{A}_{\mathrm{n}} =\left(\mathrm{2}+\sqrt{\mathrm{2}}\right)^{\mathrm{n}} =\left(\mathrm{m}_{\mathrm{n}}…
Question Number 35915 by Rio Mike last updated on 25/May/18 $${if}\:{P}\left({A}\right)\:{and}\:{P}\left({B}\right)\:{are}\:{independent} \\ $$$${events}\:{then}\:{P}\left({A}\mid{B}\right)=?? \\ $$ Answered by $@ty@m last updated on 26/May/18 $${P}\left({A}\diagup{B}\right)=\frac{{P}\left({A}\cap{B}\right)}{{P}\left({B}\right)}\:….\left({i}\right) \\ $$$$\because\:{P}\left({A}\right)\:{and}\:{P}\left({B}\right)\:{are}\:{independent}…
Question Number 35811 by Rio Mike last updated on 23/May/18 $$\:{Multiple}\:{Choice}\:{Questions} \\ $$$$\:\:\:\boldsymbol{{Rio}}\:\boldsymbol{{M}}{ike}. \\ $$$$ \\ $$$${Q}_{\mathrm{1}} .\:{The}\:{value}\:{of}\:\:\mathrm{6}\:+\:\mathrm{2}\:×\:\mathrm{4}\:−\mathrm{15}\:\boldsymbol{\div}\:\mathrm{3} \\ $$$${is}; \\ $$$$\left.{A}\left.\right)\left.\:\left.\mathrm{3}\:\:{B}\right)\:\mathrm{9}\:{C}\right)\:\mathrm{4}\:{D}\right)\:\mathrm{27} \\ $$$$ \\…
Question Number 101330 by 175 last updated on 01/Jul/20 $${Evaluate}. \\ $$$$\int_{−\pi} ^{\pi} {x}^{\mathrm{9}} \mathrm{cos}\:{x}\:{dx} \\ $$ Commented by mr W last updated on 01/Jul/20…
Question Number 101329 by 175 last updated on 01/Jul/20 Answered by mr W last updated on 03/Jul/20 $$\left(\mathrm{90}−\mathrm{35}\right)×{t}=\mathrm{35}×\frac{\mathrm{3}}{\mathrm{4}} \\ $$$${t}=\frac{\mathrm{21}}{\mathrm{44}}\:{hours} \\ $$$$\mathrm{90}×\frac{\mathrm{21}}{\mathrm{44}}=\mathrm{42}.\mathrm{95}\:{km} \\ $$$${they}\:{traveld}\:\mathrm{42}.\mathrm{95}\:{km}\:{when}\:{they}\:{met}. \\…
Question Number 35738 by Rio Mike last updated on 22/May/18 $$\:{Given}\:{that}\:\:\int_{\mathrm{0}} ^{{k}} {x}^{\mathrm{2}} =\:\mathrm{16} \\ $$$${find}\:{the}\:{value}\:{of}\:{k} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 22/May/18…