Chapter14Sec2

# Chapter14Sec2 - Initialization Cells(Code Needed for Most...

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Initialization Cells (Code Needed for Most Plot3D Statements) In[7]:= ticks @ min_, max_ D : = Join @ Table @8 i,If @ i 0, ,Style @ i,12 DD , 8 0.01,0 << , 8 i,Ceiling @ min D ,Floor @ max D , 2 <D , H * Numbered ticks * L Table @8 j, , 8 0.01,0 << , 8 j,Round @ min D ,Round @ max - 1 D ,1 <DD H * Un - numbered ticks * L H * 2D Options * L SetOptions @ Plot, ImageSize fi 350, AxesOrigin fi 8 0,0 < , AspectRatio fi 1, AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks D ; H * 3D Options * L SetOptions @ Plot3D, ImageSize fi 600, BoxRatios fi 1,Boxed fi False, AxesOrigin fi 8 0,0,0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None, ViewPoint fi 8 2,0.9,1 < , ViewVertical fi 8 0,0,1 < D ; SetOptions @ ContourPlot3D, ImageSize fi 600, BoxRatios fi 1,Boxed fi False, AxesOrigin fi 8 0,0,0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None, ViewPoint fi 8 2,0.9,1 < , ViewVertical fi 8 0,0,1 < D ; SetOptions @ ParametricPlot3D, ImageSize fi 600, BoxRatios fi 1,Boxed fi False, AxesOrigin fi 8 0,0,0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None,

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ViewPoint fi 8 2,0.9,1 < , ViewVertical fi 8 0,0,1 < D ; SetOptions @ RegionPlot3D, ImageSize fi 600, BoxRatios fi 1,Boxed fi False, AxesOrigin fi 8 0,0,0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None, ViewPoint fi 8 2,0.9,1 < , ViewVertical fi 8 0,0,1 < D ; Chapter 14: Partial Derivatives 2 Chapter14Sec2.nb
Section 14.2: Limits and Continuity Limits ª Definition Let f be a function of two variables whose domain D includes points arbitrarily close to H a , b L (but not necessarily the point H a , b L . Then we say that the limit of f H x , y L as H x , y L approaches H a , b L is L , and we write lim H x , y L fi H a , b L f H x , y L = L if for every number Ε > 0, there exists a corresponding number Δ > 0 such that if H x , y L ˛ D and 0 < H x , y L - H a , b L/ < Δ , then f H x , y L - L / < Ε .

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