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Category: Differentiation

Question-172785

Question Number 172785 by mnjuly1970 last updated on 01/Jul/22 Answered by Eulerian last updated on 01/Jul/22 $$\: \\ $$$$\:\mathrm{Note}:\:\:\mathrm{H}_{\mathrm{n}−\mathrm{1}} \:=\:\gamma\:+\:\psi^{\left(\mathrm{0}\right)} \left(\mathrm{n}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{H}_{\mathrm{n}−\mathrm{1}} \:=\:\mathrm{H}_{\mathrm{n}} \:−\:\frac{\mathrm{1}}{\mathrm{n}}…

Question-172681

Question Number 172681 by mnjuly1970 last updated on 30/Jun/22 Answered by Jamshidbek last updated on 30/Jun/22 $$\mathrm{Hint}:\:\mathrm{Lemma}:\:\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{f}\left(\mathrm{a}+\mathrm{b}−\mathrm{x}\right)\mathrm{dx} \\ $$$$\mathrm{after}\:\mathrm{tg}\frac{\mathrm{x}}{\mathrm{2}}=\mathrm{t}. \\ $$…

min-y-9-sin-2-x-4-csc-2-x-3-

Question Number 172613 by cortano1 last updated on 29/Jun/22 $$\:\:\:{min}\:{y}=\mathrm{9}\:\mathrm{sin}\:^{\mathrm{2}} {x}+\:\mathrm{4}\:{csc}^{\mathrm{2}} {x}\:+\:\mathrm{3} \\ $$ Answered by Rasheed.Sindhi last updated on 29/Jun/22 $${y}=\left(\mathrm{3sin}\:{x}+\mathrm{2}\:\mathrm{csc}\:{x}\right)^{\mathrm{2}} −\mathrm{12}+\mathrm{3} \\ $$$${y}=\left(\mathrm{3sin}\:{x}+\mathrm{2}\:\mathrm{csc}\:{x}\right)^{\mathrm{2}}…

Question-172359

Question Number 172359 by mnjuly1970 last updated on 25/Jun/22 Answered by Mathspace last updated on 26/Jun/22 $${J}=\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{−\frac{\mathrm{1}}{\mathrm{2}}} \left(\mathrm{1}−{x}\right)^{−\frac{\mathrm{1}}{\mathrm{2}}} {ln}^{\mathrm{2}} {xdx} \\ $$$${let}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}}…