Menu Close

Category: Differentiation

Find-concave-up-and-concove-down-of-function-f-x-x-2-x-3-

Question Number 121956 by bemath last updated on 13/Nov/20 $${Find}\:{concave}\:{up}\:{and}\:{concove}\:{down} \\ $$$${of}\:{function}\:{f}\left({x}\right)\:=\:{x}^{\mathrm{2}} \:\mid{x}−\mathrm{3}\mid\: \\ $$ Answered by MJS_new last updated on 13/Nov/20 $${f}\left({x}\right)=\begin{cases}{\mathrm{3}{x}^{\mathrm{2}} −{x}^{\mathrm{3}} ;\:{x}<\mathrm{3}}\\{{x}^{\mathrm{3}}…

advanced-calculus-evaluate-I-0-pi-2-ln-tan-x-sin-x-cos-x-2-dx-m-n-

Question Number 121869 by mnjuly1970 last updated on 12/Nov/20 $$\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\overset{???} {=}\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \left(\frac{{ln}\left({tan}\left({x}\right)\right)}{{sin}\left({x}\right)−{cos}\left({x}\right)}\right)^{\mathrm{2}} {dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.{m}.{n}. \\ $$ Answered by mindispower…

Question-121729

Question Number 121729 by oustmuchiya@gmail.com last updated on 11/Nov/20 Answered by bemath last updated on 11/Nov/20 $$\left({i}\right)\:\mathrm{2}{yy}'+\mathrm{3}{x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} {y}'=\mathrm{3}{y}' \\ $$$$\Leftrightarrow\:\mathrm{3}{x}^{\mathrm{2}} \:=\:{y}'\left(\mathrm{3}+\mathrm{3}{y}^{\mathrm{2}} −\mathrm{2}{y}\right) \\ $$$$\Leftrightarrow\:{y}'\:=\:\frac{\mathrm{3}{x}^{\mathrm{2}}…

advanced-calculus-please-prove-0-arctan-2x-1-x-2-dx-x-piln-1-2-m-n-

Question Number 121713 by mnjuly1970 last updated on 11/Nov/20 $$\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$$\:{please}\:\:{prove}: \\ $$$$\Phi=\int_{\mathrm{0}} ^{\:\infty} {arctan}\left(\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)\frac{{dx}}{{x}}\:=\pi{ln}\left(\mathrm{1}+\sqrt{\mathrm{2}}\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{m}.{n}… \\ $$ Terms of Service Privacy…

please-evaluate-i-1-0-e-x-ln-1-e-x-dx-ii-2-0-sin-x-x-3-dx-iii-n-1-1-n-n-2-cos-n-2-pi-2-9-

Question Number 121649 by mnjuly1970 last updated on 10/Nov/20 $$\:\:\:\:\:\:\:\:{please}\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:{i}:\:\:\:\Omega_{\mathrm{1}} \:\overset{?} {=}\int_{\mathrm{0}} ^{\:\infty} {e}^{−{x}} {ln}\left(\Gamma\left(\mathrm{1}−{e}^{−{x}} \right)\right){dx} \\ $$$$\:\:\:\:\:\:\:{ii}:\:\:\:\Omega_{\mathrm{2}} \overset{?} {=}\int_{\mathrm{0}} ^{\:\infty} \left(\frac{{sin}\left({x}\right)}{{x}}\right)^{\mathrm{3}} {dx}…

Find-the-expansion-and-the-convergemce-of-the-following-in-the-power-of-x-i-sinx-ii-ln-1-x-iii-tan-1-x-

Question Number 56069 by necx1 last updated on 09/Mar/19 $${Find}\:{the}\:{expansion}\:{and}\:{the}\:{convergemce} \\ $$$${of}\:{the}\:{following}\:{in}\:{the}\:{power}\:{of}\:{x}: \\ $$$$\left({i}\right){sinx} \\ $$$$\left({ii}\right)\mathrm{ln}\:\left(\mathrm{1}+{x}\right) \\ $$$$\left({iii}\right)\mathrm{tan}^{−\mathrm{1}} {x} \\ $$ Commented by tanmay.chaudhury50@gmail.com last…

How-do-you-make-a-curve-y-ax-3-bx-2-cx-d-with-a-critical-point-of-1-0-and-2-27-

Question Number 187053 by horsebrand11 last updated on 13/Feb/23 $$\:{How}\:{do}\:{you}\:{make}\:{a}\:{curve}\: \\ $$$$\:{y}={ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}\:{with}\:{a}\:{critical} \\ $$$$\:{point}\:{of}\:\left(\mathrm{1},\mathrm{0}\right)\:{and}\:\left(−\mathrm{2},\mathrm{27}\right)\:? \\ $$ Answered by cortano12 last updated on 13/Feb/23…