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Category: Vector Calculus

A-ball-lies-on-the-function-z-xy-at-the-point-1-2-2-Find-the-point-in-the-xy-plane-where-the-ball-will-touch-it-Calculus-2-problem-

Question Number 200929 by Akira181 last updated on 26/Nov/23 $$\mathrm{A}\:\mathrm{ball}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{function}\:{z}={xy}\:\mathrm{at} \\ $$$$\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{2},\mathrm{2}\right).\:\mathrm{Find}\:\mathrm{the}\:\mathrm{point}\:\mathrm{in} \\ $$$$\mathrm{the}\:{xy}−\mathrm{plane}\:\mathrm{where}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{will} \\ $$$$\mathrm{touch}\:\mathrm{it}. \\ $$$$\mathrm{Calculus}\:\mathrm{2}\:\mathrm{problem}. \\ $$ Commented by Akira181 last updated…

Question-193204

Question Number 193204 by Mingma last updated on 07/Jun/23 Answered by witcher3 last updated on 08/Jun/23 $$\mathrm{H}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{k}}=\overset{\mathrm{1}} {\int}_{\mathrm{0}} \underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{x}^{\mathrm{k}−\mathrm{1}} \mathrm{dx}…

lim-x-0-x-x-1-xlnx-

Question Number 64011 by Prithwish sen last updated on 12/Jul/19 $$\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{m}}\frac{\mathrm{x}^{\mathrm{x}} −\mathrm{1}}{\mathrm{xlnx}} \\ $$ Commented by kaivan.ahmadi last updated on 12/Jul/19 $${y}={x}^{{x}} \Rightarrow{lny}={xlnx}\Rightarrow\frac{{y}'}{{y}}={lnx}+{x}×\frac{\mathrm{1}}{{x}}=\mathrm{1}+{lnx}\Rightarrow \\…

find-S-F-n-ds-where-F-y-2-i-yj-xzk-and-S-is-the-upper-half-of-the-sphere-x-2-y-2-z-2-a-2-

Question Number 128691 by BHOOPENDRA last updated on 09/Jan/21 $${find}\int\int_{{S}} \bigtriangledown×{F}\:.\hat {{n}ds} \\ $$$${where}\:{F}^{\rightarrow} ={y}^{\mathrm{2}} \hat {{i}}+{y}\hat {{j}}−{xz}\hat {{k}} \\ $$$${and}\:{S}\:{is}\:{the}\:{upper}\:{half}\:{of}\:{the}\:{sphere} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}}…