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Category: Differentiation

Question-126635

Question Number 126635 by BHOOPENDRA last updated on 22/Dec/20 Answered by Ar Brandon last updated on 22/Dec/20 $$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{r}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \theta\mathrm{cos}^{\mathrm{2}} \phi+\mathrm{r}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}}…

calculus-prove-that-0-1-x-n-1-ln-2-1-x-dx-2-n-k-1-n-H-k-k-

Question Number 126631 by mnjuly1970 last updated on 23/Dec/20 $$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{calculus}… \\ $$$$\:\:\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:::\:\:\:\:\:\:\Omega\overset{??} {=}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}^{{n}−\mathrm{1}} {ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right){dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{2}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{{H}_{{k}}…

Let-P-be-point-on-the-graph-of-a-straight-line-y-2x-3-and-Q-be-a-point-on-the-graph-of-a-parabola-y-x-2-x-1-Find-the-shortest-distance-between-P-and-Q-

Question Number 126605 by bramlexs22 last updated on 22/Dec/20 $$\:{Let}\:{P}\:{be}\:{point}\:{on}\:{the}\:{graph}\: \\ $$$${of}\:{a}\:{straight}\:{line}\:{y}=\mathrm{2}{x}−\mathrm{3}\:{and}\:{Q} \\ $$$${be}\:{a}\:{point}\:{on}\:{the}\:{graph}\:{of}\:{a}\:{parabola} \\ $$$${y}={x}^{\mathrm{2}} +{x}+\mathrm{1}\:.{Find}\:{the}\:{shortest}\: \\ $$$${distance}\:{between}\:{P}\:{and}\:{Q}\:. \\ $$ Answered by liberty last…

Question-126524

Question Number 126524 by rs4089 last updated on 21/Dec/20 Answered by Olaf last updated on 21/Dec/20 $$\mathrm{Let}\:{u}\:=\:{e}^{{x}} \\ $$$$\frac{{dy}}{{dx}}\:=\:\frac{{dy}}{{du}}.\frac{{du}}{{dx}}\:=\:{e}^{{x}} \frac{{dy}}{{du}}\:=\:{u}\frac{{dy}}{{du}} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:=\:\frac{{d}}{{dx}}\left(\frac{{du}}{{dx}}\right)\:=\:\frac{{d}}{{du}}\left({u}\frac{{du}}{{du}}\right)\frac{{du}}{{dx}} \\…

If-Q-2-x-y-1-5-x-lt-1-5-y-lt-6-Find-Q-max-

Question Number 192054 by cortano12 last updated on 07/May/23 $$\:\:\:\mathrm{If}\:\mathrm{Q}\:=\:\frac{\mathrm{2}−\mathrm{x}}{\mathrm{y}−\mathrm{1}}\:;\:−\mathrm{5}\leqslant\mathrm{x}<−\mathrm{1}\:,\:\mathrm{5}\leqslant\mathrm{y}<\mathrm{6} \\ $$$$\:\:\:\mathrm{Find}\:\mathrm{Q}_{\mathrm{max}} .\: \\ $$ Answered by mehdee42 last updated on 07/May/23 $$−\mathrm{5}\leqslant{x}<−\mathrm{1}\overset{×−\mathrm{1}} {\Rightarrow}\:\mathrm{1}<−{x}\leqslant\mathrm{5}\overset{+\mathrm{2}} {\Rightarrow}\mathrm{3}<\mathrm{2}−{x}\leqslant\mathrm{7}\:\:\left({i}\right)…