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Category: Differentiation

Question-197057

Question Number 197057 by ajfour last updated on 07/Sep/23 Commented by ajfour last updated on 07/Sep/23 $${The}\:{ant}\:{has}\:{to}\:{climb}\:{up}\:{the}\:{plane} \\ $$$${and}\:{surmount}\:{the}\:{wall}\:{of}\:{height}\:{c}, \\ $$$${and}\:{descend}\:{then}\:{reach}\:{B}.\:{Find}\:{the} \\ $$$${shortest}\:{length}\:{of}\:{path}. \\ $$…

m-1-n-1-1-n-1-m-2-n-mn-2-

Question Number 195952 by mnjuly1970 last updated on 13/Aug/23 $$ \\ $$$$\:\:\:\:\Omega\:=\:\underset{{m}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\:{n}+\mathrm{1}} }{{m}^{\mathrm{2}} {n}\:+\:{mn}^{\:\mathrm{2}} }\:\:=\:?\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:−−−−− \\ $$ Answered by…

dy-dx-1-y-2-1-x-2-0-

Question Number 195885 by cortano12 last updated on 12/Aug/23 $$\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\sqrt{\frac{\mathrm{1}−\mathrm{y}^{\mathrm{2}} }{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:=\:\mathrm{0}\: \\ $$ Answered by mokys last updated on 12/Aug/23 $$\frac{{dy}}{\:\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }}\:+\:\frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:=\:{d}\left(\mathrm{0}\right) \\…