11.16.2237f is differentiable at yo if thefollowing limitexistsl im x f Xoxoxo X Xox this is considered f Xoalso there exists a number m and afunction E x such thatf x f Xo MIX Xo E X X XoWe can expand thisnotion of diffrentiabilityto 2 variablesbyconsideringtangentplanesinstead oftangent lines to thefunctionIf f is a functionof two variablesdefined on an open diskWI center Xoyo f is differientiable itf x y f Xoyo fx Xoyo x Xo t fyXoyo y yo t E x y x Xo Ez xyy yoTanepassingthroughlyIf f hasfirst orderpartials eachpt in a diskcenteredXo yo and if these partials are continuous xo yothen f is differentiable at xo yoLesson37 Problems1 D 2 D 3 C
