Question Number 138819 by qaz last updated on 18/Apr/21 $$\left(\mathrm{1}\right)::{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \mid{x}−\mathrm{2}{t}\mid{dt},\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{3}} {f}\left({x}\right){dx}=? \\ $$$$−−−−−−−−−−−−−−−−−−− \\ $$$$\left(\mathrm{2}\right)::{f}\left({x}\right)={x}^{\mathrm{2}} \centerdot\int_{\mathrm{1}} ^{{x}} \frac{{dt}}{{t}^{\mathrm{3}} −\mathrm{3}{t}^{\mathrm{2}} +\mathrm{3}{t}},\:\:\:\:\:\:\:\:\:\:\:\:\:{f}^{\left(\mathrm{2019}\right)} \left(\mathrm{1}\right)=? \\…
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Question Number 7743 by Tawakalitu. last updated on 13/Sep/16 $${All}\:{the}\:{terms}\:{of}\:{the}\:{arithmetic}\:{progession}\: \\ $$$${u}_{\mathrm{1}} ,\:{u}_{\mathrm{2}} ,\:{u}_{\mathrm{3}} ,\:…\:{u}_{{n}} \:\:{are}\:{positive}\:.\:{use}\:{induction}\:{to} \\ $$$${prove}\:{that}\:{for}\:{n}\:\geqslant\:\mathrm{2} \\ $$$$\frac{\mathrm{1}}{{u}_{\mathrm{1}} {u}_{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{u}_{\mathrm{2}} {u}_{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{{u}_{\mathrm{3}} {u}_{\mathrm{4}}…
Question Number 73279 by byaw last updated on 09/Nov/19 Answered by mr W last updated on 09/Nov/19 $$\mathrm{40}={v}_{\mathrm{0}} ×\mathrm{4}+\frac{\mathrm{1}}{\mathrm{2}}{a}×\mathrm{4}^{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{10}={v}_{\mathrm{0}} +\mathrm{2}{a}\:\:\:…\left({i}\right) \\ $$$$\mathrm{72}={v}_{\mathrm{0}} ×\mathrm{6}+\frac{\mathrm{1}}{\mathrm{2}}{a}×\mathrm{6}^{\mathrm{2}}…
Question Number 73274 by peter frank last updated on 09/Nov/19 Commented by kaivan.ahmadi last updated on 09/Nov/19 $${t}=\mathrm{0}\Rightarrow{x}=\mathrm{1}\:,\:{y}=\mathrm{0}\Rightarrow \\ $$$$\frac{\partial{f}}{\partial{t}}=\frac{\partial{f}}{\partial{x}}×\frac{\partial{x}}{\partial{t}}+\frac{\partial{f}}{\partial{y}}×\frac{\partial{y}}{\partial{t}}= \\ $$$$\left({siny}+{e}^{{x}} {cosy}\right)\left(\mathrm{2}{t}\right)+\left({xcosy}−{e}^{{x}} {siny}\right)\left(\mathrm{2}{t}\right)\mid_{{t}=\mathrm{0}} =…
Question Number 7739 by upendrakishor99@gmail.com last updated on 13/Sep/16 $${Ifz}_{\mathrm{1}} ,{z}_{\mathrm{2}} {be}\:{complex}\:{numbers},\:{prove}\:{that} \\ $$$${tan}\left({z}_{\mathrm{1}} +{z}_{\mathrm{2}} \right)={tanz}_{\mathrm{1}} +{tanz}_{\mathrm{2}} /\mathrm{1}−{tanz}_{\mathrm{1}} {tanz}_{\mathrm{2}} \\ $$$$ \\ $$$$ \\ $$…
Question Number 73275 by solihin last updated on 09/Nov/19 $$ \\ $$$$ \\ $$$$\int\frac{\mathrm{4}}{{x}^{\mathrm{2}} \sqrt{\mathrm{4}−{x}\delta\varkappa}}\:\:\:\:? \\ $$$$ \\ $$ Commented by MJS last updated on…
Question Number 7738 by 314159 last updated on 13/Sep/16 Commented by Rasheed Soomro last updated on 13/Sep/16 $$\frac{\mathrm{248}\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right)^{\mathrm{2}} +\mathrm{496}\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{4}}}\right)^{\mathrm{6}} +\mathrm{1984}\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{8}}}\right)^{\mathrm{8}} +…}{\mathrm{1}+\mathrm{5}+\mathrm{9}+…\mathrm{393}} \\ $$$$\frac{\mathrm{248}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{1}} +\mathrm{496}\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{3}} +\mathrm{1984}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)^{\mathrm{4}}…
Question Number 138810 by mathdanisur last updated on 18/Apr/21 $$\underset{\:\mathrm{0}} {\overset{\:\pi/\mathrm{2}} {\int}}\frac{{xsin}\left({x}\right)}{\mathrm{1}−{cosx}}\centerdot{log}\left(\mathrm{1}+{cosx}\right){dx}=? \\ $$ Answered by phanphuoc last updated on 18/Apr/21 $${u}={x},{dv}={ln}\left(\mathrm{1}+{cosx}\right){dcosx}/\left(\mathrm{1}−{cosx}\right) \\ $$ Commented…
Question Number 73273 by peter frank last updated on 09/Nov/19 Answered by MJS last updated on 09/Nov/19 $$\mathrm{tricky}… \\ $$$${x}^{\mathrm{2}} −\mathrm{cos}\:\mathrm{2}{x}\:−\mathrm{1}= \\ $$$$={x}^{\mathrm{2}} −\mathrm{2cos}^{\mathrm{2}} \:{x}\:=…