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Category: Differentiation

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)…

find-w-and-w-given-that-w-x-y-z-f-x-2-y-2-z-2-where-x-rcos-cos-y-rcos-sin-z-rsin-

Question Number 126478 by BHOOPENDRA last updated on 20/Dec/20 $${find}\:\frac{\partial{w}}{\partial\theta}\:{and}\:\frac{\partial{w}}{\partial\phi}\:{given}\:{that}\: \\ $$$${w}\left({x},{y},{z}\right)={f}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)\:{where}\:{x}={rcos}\theta{cos}\phi \\ $$$${y}={rcos}\theta{sin}\phi,{z}={rsin}\theta. \\ $$ Terms of Service Privacy Policy Contact:…

advanced-calculus-prove-that-n-2-1-1-n-4-cosh-2-pi-cos-2-pi-4pi-2-

Question Number 126440 by mnjuly1970 last updated on 20/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:{prove}\:\:{that}\:::: \\ $$$$\:\:\:\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{4}} }\:\right)=\frac{{cosh}\left(\sqrt{\mathrm{2}}\:\pi\right)−{cos}\left(\sqrt{\mathrm{2}}\:\pi\right)}{\mathrm{4}\pi^{\mathrm{2}} } \\ $$$$ \\ $$ Answered by Dwaipayan…

Question-126070

Question Number 126070 by benjo_mathlover last updated on 17/Dec/20 Commented by liberty last updated on 17/Dec/20 $${h}\left({x}\right)=\int_{\mathrm{1}} ^{\:{x}} {f}\left({t}\right)\:{dt}\:\Leftrightarrow\:{h}'\left({x}\right)=\:{f}\left({x}\right) \\ $$$${h}'\left(\mathrm{4}\right)={f}\left(\mathrm{4}\right)=\:\mathrm{2} \\ $$$$ \\ $$…