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Question-133341

Question Number 133341 by mohammad17 last updated on 21/Feb/21 Answered by mathmax by abdo last updated on 21/Feb/21 $$\left.\mathrm{1}\right)\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{3}} \:+\mathrm{4x}^{\mathrm{2}} −\mathrm{10}\:\:\:\:\Rightarrow\mathrm{f}^{'} \left(\mathrm{x}\right)=\mathrm{3x}^{\mathrm{2}} \:+\mathrm{8x}\:>\mathrm{0}\:\mathrm{on}\left[\mathrm{1},\mathrm{2}\right]\:\Rightarrow\mathrm{f}\:\mathrm{is}\:\mathrm{increazing} \\ $$$$\mathrm{on}\:\left[\mathrm{1},\mathrm{2}\right]\:\mathrm{we}\:\mathrm{have}\:\mathrm{f}\left(\mathrm{1}\right)=\mathrm{5}−\mathrm{10}=−\mathrm{5}<\mathrm{0}\:\mathrm{and}\:\mathrm{f}\left(\mathrm{2}\right)=\mathrm{8}+\mathrm{16}−\mathrm{10}=\mathrm{14}>\mathrm{0}\:\Rightarrow…

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Question Number 133334 by mnjuly1970 last updated on 21/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:\:\:\:\:{calculus}… \\ $$$$\:{prove}\:\:{that}:: \\ $$$$\:\:\:\boldsymbol{\phi}=\int_{−\infty} ^{\:+\infty} \frac{\:{cosh}\left({px}\right)}{{cosh}\left({x}\right)}\:=\:\frac{\pi}{{cos}\left(\frac{\pi{p}}{\mathrm{2}}\right)} \\ $$$$ \\ $$ Answered by mnjuly1970 last updated…

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Question Number 67795 by mathmax by abdo last updated on 31/Aug/19 $${let}\:\:{A}_{{p}} =\int_{\mathrm{0}} ^{\pi} \:{x}^{{p}} \:{cos}\left({nx}\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{0}} ,{A}_{\mathrm{1}} ,{A}_{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right){determine}\:{a}\:{relation}\:{of}\:{recurrence}\:{between}\:\:{A}_{{p}} \\ $$ Commented…