1 if x+yO ifx-yf(x,y) if (x,y) eEALet A -[0,1]x[0, 1] and f:A-R be defined by f(x,V) =-Define an extension 7:R -R by 7 (x,)-if (x,) ER?\AMark all answers that are correct.Function f is Riemann integrable over A andS fox,v)dxdy = 1.The functian f is nat Riemann integrable aver A since the set of paints where f is discontinuaus dAU((x,y) ER :x = v) does nat have measure zero.Is discontinuous at Xp ER? If and only if Xo E JAU((x,V) ER? : x = y}. Moreover, the set dAU{(x.y) E R?: x- y) has measure zero.:x = v), the ascillation of f at Xo equals 1. i.e. w;(xo) = 1.

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1 ifx+y fx,y) if (x,y)EA Let A- [0,1]x[0,1] and f:A-R be defined by f(x,y) = . Define an extension 7:R -R by F(x,v) - O ifx=y if (x,V) ER\A Mark all answers that are correct. O Function f is Riemann integrable over A and fx,y)dxdy = 1. O The function f is not Riemann integrabie over A since the set of points where s dscontinuous 3Au[(x,y) ER? :x=v) does not have measure zero. o řsdscontmuous at Xo ER?ifand only if XoedAux,y) ER? : x=y). Moreover, the set JAU{(x,y)ER?:x-y}has measure zero. O For every Xo €dAU[(x,V) ER:x= yl the oscillation of f at xo equals 1, ie. w;(xo) =1.

1 ifx+y fx,y) if (x,y)EA Let A- [0,1]x[0,1] and f:A-R be defined by f(x,y) = . Define an extension 7:R -R by F(x,v) - O ifx=y if (x,V) ER\A Mark all answers that are correct. O Function f is Riemann integrable over A and fx,y)dxdy = 1. O The function f is not Riemann integrabie over A since the set of points where s dscontinuous 3Au[(x,y) ER? :x=v) does not have measure zero. o řsdscontmuous at Xo ER?ifand only if XoedAux,y) ER? : x=y). Moreover, the set JAU{(x,y)ER?:x-y}has measure zero. O For every Xo €dAU[(x,V) ER:x= yl the oscillation of f at xo equals 1, ie. w;(xo) =1.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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