Question Number 75066 by ~blr237~ last updated on 06/Dec/19 $$\mathrm{Prove}\:\:\mathrm{that}\:\mathrm{if}\:\:\mathrm{f}\:\mathrm{is}\:\mathrm{a}\:\mathrm{function}\:\mathbb{R}\rightarrow\mathbb{R}\: \\ $$$$\mathrm{and}\:\:\mathrm{there}\:\mathrm{exist}\:\mathrm{x}_{\mathrm{0}} >\mathrm{0}\:\:,\:\mathrm{such}\:\mathrm{as}\:\:\mathrm{L}\left(\mathrm{f}\right)\left(\mathrm{x}_{\mathrm{0}} \right)\:\mathrm{exist}\: \\ $$$$\mathrm{then}\:\underset{\mathrm{t}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{t}\right)\mathrm{e}^{−\mathrm{x}_{\mathrm{0}} \mathrm{t}} =\mathrm{0}\:\mathrm{and}\:\forall\:\mathrm{x}>\mathrm{x}_{\mathrm{0}} \:\:\mathrm{L}\left(\mathrm{f}\right)\left(\mathrm{x}\right)\:\mathrm{exist}. \\ $$$$\mathrm{L}\left(\mathrm{f}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{Laplace}\:\mathrm{transformed}\:\mathrm{function} \\ $$ Answered…
Question Number 75041 by ~blr237~ last updated on 06/Dec/19 $$\left.\mathrm{1}\left.\right)\left.\:\mathrm{Show}\:\mathrm{that}\:\:\mathrm{for}\:\mathrm{a}\in\right]\mathrm{01}\right]\mathrm{the}\:\mathrm{function}\:\:\mathrm{f}_{\mathrm{a}} \::\mathbb{R}_{+} \rightarrow\mathbb{R}\:\mathrm{defined}\:\mathrm{by}\:\mathrm{f}_{\mathrm{a}} \left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{a}} \: \\ $$$$\mathrm{is}\:\:\:\mathrm{a}−\mathrm{holder}\:\mathrm{function}\:\:\mathrm{in}\:\mathrm{other}\:\mathrm{way}\:\:\mathrm{there}\:\mathrm{exist}\:\:\mathrm{K}>\mathrm{0}\:\mathrm{such}\:\mathrm{as}\:\forall\:\mathrm{x},\mathrm{y}>\mathrm{0}\: \\ $$$$\mid\mathrm{f}_{\mathrm{a}} \left(\mathrm{x}\right)−\mathrm{f}_{\mathrm{a}} \left(\mathrm{y}\right)\mid\leqslant\mathrm{K}\mid\mathrm{x}−\mathrm{y}\mid^{\mathrm{a}} \:\: \\ $$$$ \\ $$…
Question Number 140571 by liberty last updated on 09/May/21 $$\int\:\left(\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}\:\right)\mathrm{dx}\:=? \\ $$ Answered by bramlexs22 last updated on 09/May/21 Answered by physicstutes last…
Question Number 9491 by Raja Naik last updated on 10/Dec/16 $$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{\mathrm{acos}^{\mathrm{3}} \mathrm{x}}{\mathrm{3sinx}^{\mathrm{2}} \:}\right) \\ $$$$\mathrm{and}\:\mathrm{it}\:\mathrm{is}\:\mathrm{possible}\:\mathrm{or}\:\mathrm{not} \\ $$ Answered by mrW last updated on 11/Dec/16 $$\mathrm{y}=\frac{\mathrm{acos}^{\mathrm{3}}…
Question Number 140550 by liberty last updated on 09/May/21 Commented by mr W last updated on 09/May/21 $${what}\:{do}\:{you}\:{get}\:{with}\:{this}\:{example}: \\ $$$${x}=−\mathrm{135} \\ $$$${y}=\mathrm{100} \\ $$$${which}\:{fulfills}\:\mathrm{3}{x}+\mathrm{4}{y}=\mathrm{5},\:{but} \\…
Question Number 74980 by ~blr237~ last updated on 05/Dec/19 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{n}\in\mathbb{N}^{\ast} \\ $$$$\:\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\:\left[\mathrm{x}+\frac{\mathrm{p}}{\mathrm{n}}\right]=\left[\mathrm{nx}\right] \\ $$ Answered by mind is power last updated on 05/Dec/19…
Question Number 140498 by mnjuly1970 last updated on 08/May/21 $$\:\:\:\:\:\:……..\:{nice}\:\:\:…….\:\:{calculus}……. \\ $$$$\:\:\:\:\:\:{simplify}: \\ $$$$\:\:\:\:\boldsymbol{\phi}\left({x}\right):=\:{sin}\left(\frac{{x}}{\mathrm{2}}\right)\left(\mathrm{1}+\mathrm{2}\underset{{m}=\mathrm{1}} {\overset{{n}} {\sum}}{cos}\left({mx}\right)\right) \\ $$$$\:\:\:\: \\ $$ Answered by Dwaipayan Shikari last…
Question Number 74959 by aliesam last updated on 04/Dec/19 $${f}\left({x}\right)=\mid{x}+\mathrm{5}\mid−\mid{x}−\mathrm{2}\mid−\mid{x}+\mathrm{6}\mid \\ $$$$ \\ $$$${find}\:{f}'\left({x}\right) \\ $$ Commented by mathmax by abdo last updated on 04/Dec/19…
Question Number 140488 by meetbhavsar25 last updated on 08/May/21 Commented by meetbhavsar25 last updated on 08/May/21 $${mr}\:{W},\:{please}\:{help}\:{me}\:{out} \\ $$ Commented by mr W last updated…
Question Number 74933 by imelder last updated on 04/Dec/19 $$\mathrm{differentiate}\:\mathrm{the}\:\mathrm{following}\:\mathrm{functions} \\ $$$$\left.\mathrm{a}\right)\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}^{\mathrm{5}} \:\mathrm{coshx} \\ $$ Commented by mathmax by abdo last updated on 04/Dec/19 $${f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{5}}…