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 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, 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 < H x , y L-H a , b L/ < Δ , then f H x , y L-L / < Ε . 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 fi a f H x L = L if and only if for every number Ε > 0, there exists a corrseponding number Δ > 0 such that if x ˛ D and 0 < x-a / < Δ , then f H x L-L / < Ε ....
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This note was uploaded on 01/13/2012 for the course MATH 333 taught by Professor Keithemmert during the Fall '11 term at Tarleton.

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Chapter14Sec2ShowCode - Initialization Cells(Code Needed...

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