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Category: Differentiation

if-g-x-x-2-x-2x-1-D-g-1-lim-x-g-1-x-ax-b-b-a-a-lt-0-then-find-the-value-of-Max-b-D-g-Domain-

Question Number 146063 by mnjuly1970 last updated on 10/Jul/21 $$ \\ $$$$\:\:\:\:{if}\:\:{g}\left({x}\right)=\frac{{x}^{\:\mathrm{2}} −{x}}{\mathrm{2}{x}−\mathrm{1}}\:\:\:,\:{D}_{{g}} =\:\left[\mathrm{1}\:,\:\infty\right) \\ $$$$\:\:\:\:,\:{lim}_{{x}\rightarrow\infty} \frac{{g}^{\:−\mathrm{1}} \left({x}\right)}{{ax}\:+\:{b}}\:=\:{b}−{a}\:\:\left({a}\:<\mathrm{0}\:\right) \\ $$$$\:\:{then}\:{find}\:\:{the}\:{value}\:{of}\:{Max}\:\left({b}\:\right) \\ $$$$\:\: \\ $$$$\:\:{D}_{\:{g}} \:=\:{Domain}\:…

I-0-e-x-J-1-2-x-dx-J-v-x-x-v-n-0-1-n-x-2n-2-n-v-n-n-v-1-

Question Number 146054 by mnjuly1970 last updated on 10/Jul/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{I}\::=\:\int_{\mathrm{0}} ^{\:\:\infty} {e}^{\:−{x}} \:.\:\mathrm{J}_{\frac{\mathrm{1}}{\mathrm{2}}} \:\left({x}\:\right)\:{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{J}_{{v}\:} \:\left({x}\:\right)\:=\:{x}^{\:{v}} \:\underset{{n}=\mathrm{0}} {\overset{\:\infty} {\sum}}\frac{\left(−\:\mathrm{1}\:\right)^{\:{n}} \:{x}^{\:\mathrm{2}{n}} }{\mathrm{2}^{\:{n}\:+\:{v}} \:{n}\:!\:\Gamma\:\left(\:{n}\:+\:{v}\:+\mathrm{1}\:\right)}…

Question-145701

Question Number 145701 by alcohol last updated on 07/Jul/21 Commented by MJS_new last updated on 07/Jul/21 $$\mathrm{1}. \\ $$$$\mathrm{square}−\mathrm{2}×\left(\mathrm{square}−\mathrm{quarter}\:\mathrm{circle}\right)= \\ $$$$=−\mathrm{square}+\mathrm{2}×\mathrm{quarter}\:\mathrm{circle}= \\ $$$$=\mathrm{half}\:\mathrm{circle}−\mathrm{square}=\mathrm{4}^{\mathrm{2}} \pi/\mathrm{2}−\mathrm{4}^{\mathrm{2}} =…

d-dx-x-x-x-1-3-1-3-1-3-

Question Number 145620 by Study last updated on 06/Jul/21 $$\frac{{d}}{{dx}}\left(\sqrt[{\mathrm{3}}]{{x}+\sqrt[{\mathrm{3}}]{{x}+\sqrt[{\mathrm{3}}]{{x}+…}}}\right)=? \\ $$ Answered by Olaf_Thorendsen last updated on 06/Jul/21 $${y}\:=\:{f}\left({x}\right)\:=\:\sqrt[{\mathrm{3}}]{{x}+{f}\left({x}\right)}\:=\:\sqrt[{\mathrm{3}}]{{x}+{y}} \\ $$$${y}^{\mathrm{3}} \:=\:{x}+{y} \\ $$$$\mathrm{3}{y}^{\mathrm{2}}…

Advanced-Calculus-Q-Find-the-value-of-determinant-i-0-1-Ln-2-x-dx-ii-

Question Number 145602 by mnjuly1970 last updated on 06/Jul/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..\mathrm{Advanced}\:………\mathrm{Calculus}….. \\ $$$$\:\:\:\mathrm{Q}::\:\:\:\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\begin{array}{|c|c|}{\:{i}\:::\:\:\:\boldsymbol{\phi}\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{Ln}\:\left(\:\Gamma\:\left(\:\mathrm{2}\:+\:{x}\:\right)\:\right){dx}\:=\:?\:\:\:\:}\\{\:{ii}\:::\:\:\:\Omega\::=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\mathrm{1}}{\:{n}\:\left(\:\mathrm{2}{n}\:+\:\mathrm{3}\:\right)}\:=\:?}\\\hline\end{array} \\ $$$$ \\…

If-y-2-1-x-2-1-x-2-Show-that-dy-dx-2-1-y-4-1-x-4-

Question Number 14513 by tawa tawa last updated on 01/Jun/17 $$\mathrm{If}\:\:\mathrm{y}^{\mathrm{2}} \left(\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} \right)\:=\:\mathrm{1}\:−\:\mathrm{x}^{\mathrm{2}} \\ $$$$\mathrm{Show}\:\mathrm{that},\:\:\:\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{\mathrm{2}} \:=\:\frac{\mathrm{1}\:−\:\mathrm{y}^{\mathrm{4}} }{\mathrm{1}\:−\:\mathrm{x}^{\mathrm{4}} } \\ $$ Answered by mrW1 last updated…

tan-2-x-tan-4-x-dx-tan-2-x-t-t-2-t-4-dx-t-3-3-t-5-5-c-

Question Number 79964 by ubaydulla last updated on 29/Jan/20 $$\int\left(\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{tan}\:^{\mathrm{4}} {x}\right){dx}=\left[\mathrm{tan}\:^{\mathrm{2}} {x}={t}\right]=\int\left({t}^{\mathrm{2}} +{t}^{\mathrm{4}} \right){dx}=\frac{{t}^{\mathrm{3}} }{\mathrm{3}}+\frac{{t}^{\mathrm{5}} }{\mathrm{5}}+{c} \\ $$ Commented by $@ty@m123 last updated on…