Chapter14Sec2ShowCode

Chapter14Sec2ShowCode - Initialization Cells (Code Needed...

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Unformatted text preview: Initialization Cells (Code Needed for Most Plot3D Statements) In[49]:= 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 350, AxesOrigin 8 0, 0 < , AspectRatio 1, AxesStyle Directive @ Medium, Bold D , Ticks ticks D ; H * 3D Options * L SetOptions @ Plot3D, ImageSize 600, BoxRatios 1, Boxed False, AxesOrigin 8 0, 0, 0 < , AxesStyle Directive @ Medium, Bold D , Ticks ticks, Mesh None, ViewPoint 8 2, 0.9, 1 < , ViewVertical 8 0, 0, 1 < D ; SetOptions @ ContourPlot3D, ImageSize 600, BoxRatios 1, Boxed False, AxesOrigin 8 0, 0, 0 < , AxesStyle Directive @ Medium, Bold D , Ticks ticks, Mesh None, ViewPoint 8 2, 0.9, 1 < , ViewVertical 8 0, 0, 1 < D ; SetOptions @ ParametricPlot3D, ImageSize 600, BoxRatios 1, Boxed False, AxesOrigin 8 0, 0, 0 < , AxesStyle Directive @ Medium, Bold D , Ticks ticks, Mesh None, ViewPoint 8 2, 0.9, 1 < , ViewVertical 8 0, 0, 1 < D ; SetOptions @ RegionPlot3D, ImageSize 600, BoxRatios 1, Boxed False, AxesOrigin 8 0, 0, 0 < , AxesStyle Directive @ Medium, Bold D , Ticks ticks, Mesh None, ViewPoint 8 2, 0.9, 1 < , ViewVertical 8 0, 0, 1 < D ; Chapter 14: Partial Derivatives 2 Chapter14Sec2.nb Section 14.2: Limits and Continuity Limits 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 H a , b L f H x , y L = L if for every number > 0, there exists a corresponding number > 0 such that if H x , y L D and < H x , y L-H a , b L/ < , then f H x , y L-L / < . Recall that H x , y L-H a , b L/ = H x-a L 2 + H y-b L 2 , i.e., we are considering the distance between the points H x , y L and H a , b L . Also, f H x , y L-L / calculates the distance between the numbers f H x , y L and L . Let f be a function of n 3 variables whose domain is D R n . Then for a R n , we say that lim x a f H x L = L if and only if for every number > 0, there exists a corrseponding number > 0 such that if x D and 0 < x-a / < , then f H x L-L / < ....
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Chapter14Sec2ShowCode - Initialization Cells (Code Needed...

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