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Category: Differentiation

find-minimum-and-maximum-value-of-f-x-y-x-2-y-2-with-constraint-x-2-y-2-1-with-Lagrange-method-

Question Number 89805 by jagoll last updated on 19/Apr/20 $$\mathrm{find}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:=\:\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{with}\:\mathrm{constraint}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{1} \\ $$$$\mathrm{with}\:\mathrm{Lagrange}\:\mathrm{method} \\ $$ Commented by john santu…

d-dx-k-1-16-x-1-k-x-0-

Question Number 89753 by jagoll last updated on 19/Apr/20 $$\frac{\mathrm{d}}{\mathrm{dx}}\:\left(\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\mathrm{16}} {\prod}}\left(\mathrm{x}+\frac{\mathrm{1}}{\mathrm{k}}\right)\right)\underset{\:\mathrm{x}\:=\:\mathrm{0}} {\mid}\:=\:? \\ $$ Commented by mr W last updated on 19/Apr/20 $${sorry}!\:{i}\:{misread}\:\Pi\:{as}\:\Sigma. \\…

f-0-6-4-4-f-0-0-f-6-4-x-y-0-x-y-6-f-x-y-1-4-f-x-16-f-y-2-f-y-16-f-x-2-f-1-f-3-2-

Question Number 155281 by mnjuly1970 last updated on 28/Sep/21 $$ \\ $$$$\:{f}\::\left[\:\mathrm{0}\:,\:\:\mathrm{6}\right]\:\rightarrow\:\left[−\mathrm{4}\:,\:\mathrm{4}\right] \\ $$$$\:\:\:{f}\:\left(\mathrm{0}\:\right)=\mathrm{0} \\ $$$$\:\:\:\:{f}\:\left(\mathrm{6}\:\right)=\mathrm{4}\: \\ $$$$\:\:{x},\:\:{y}\geqslant\mathrm{0}\:\:,\:{x}+{y}\:\leqslant\mathrm{6} \\ $$$$\:\:\:{f}\:\left({x}+{y}\:\right)=\frac{\mathrm{1}}{\mathrm{4}}\left\{{f}\left({x}\right)\sqrt{\mathrm{16}−\left({f}\left({y}\right)\right)^{\mathrm{2}} }\:+{f}\left({y}\right)\sqrt{\mathrm{16}−\left({f}\left({x}\right)\right)^{\mathrm{2}} }\:\right\} \\ $$$$\:\:\therefore\:\:\:\left(\:{f}\left(\mathrm{1}\right)\:+{f}\:\left(\mathrm{3}\right)\right)^{\:\mathrm{2}} =?…

If-0-ln-2-x-sin-x-x-dx-prove-that-4-2-pi-3-3-m-n-

Question Number 155237 by mnjuly1970 last updated on 27/Sep/21 $$ \\ $$$$\:\:\mathrm{I}{f}\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{ln}^{\:\mathrm{2}} \left({x}\:\right).{sin}\left(\sqrt{{x}\:}\:\right)}{{x}}\:{dx} \\ $$$$\:\:\:\:\:{prove}\:{that}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega\:=\:\mathrm{4}\:\gamma^{\:\mathrm{2}} \:+\:\frac{\pi^{\:\mathrm{3}} }{\mathrm{3}}\:\:\:\:\:\blacksquare\:{m}.{n} \\ $$ Answered by…

Question-155203

Question Number 155203 by nadovic last updated on 26/Sep/21 Answered by TheHoneyCat last updated on 29/Sep/21 $$\mathrm{let}\:\mathrm{O}\:\mathrm{be}\:\mathrm{the}\:\mathrm{center}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle} \\ $$$$\mathrm{let}\:\mathrm{A}\:\mathrm{be}\:\mathrm{a}\:\mathrm{vertice}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle} \\ $$$$\mathrm{let}\:\theta\:\mathrm{be}\:\mathrm{an}\:\mathrm{angle}\:\left(\mathrm{in}\:\mathrm{radian}\right)\:\mathrm{between}\:\mathrm{one}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{two}\:\mathrm{axis}\:\left(\mathrm{O}{z}\:\mathrm{or}\:\mathrm{O}{y}\right)\:\mathrm{and}\:\mathrm{the}\:\left(\mathrm{OA}\right)\:\mathrm{line} \\ $$$$…

the-particular-integral-of-the-differential-equation-f-D-y-e-ax-where-f-D-D-a-g-D-g-a-0-is-

Question Number 23522 by gopikrishnan005@gmail.com last updated on 01/Nov/17 $${the}\:{particular}\:{integral}\:{of}\:{the}\:{differential}\:{equation}\:{f}\left({D}\right){y}={e}^{{ax}} {where}\:{f}\left({D}\right)=\left({D}−{a}\right){g}\left({D}\right),{g}\left({a}\right)\neq\mathrm{0}\:{is} \\ $$ Commented by 1kanika# last updated on 26/Nov/17 $$\mathrm{xe}\Lambda\mathrm{ax}/\mathrm{g}\left(\mathrm{a}\right) \\ $$ Terms of…