Epsilon delta proof, 3-space help

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SUMMARY

The discussion focuses on the application of epsilon-delta proofs in the context of limits in three-dimensional space. The user seeks resources to demonstrate that the function f(x) approaches a limit of 1 as (x,y) approaches (x0,y0). A key formula provided is the limit definition: \lim_{(x,y)\rightarrow(x_0,y_0)}f(x,y)=L, which requires establishing a relationship between epsilon and delta. The conversation highlights the need for specific resources tailored to three-dimensional epsilon-delta proofs.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with epsilon-delta definitions
  • Basic knowledge of functions in three-dimensional space
  • Experience with mathematical proofs
NEXT STEPS
  • Research "Epsilon-Delta Proofs in 3D" for specific examples and explanations
  • Study "Multivariable Calculus Limit Theorems" to deepen understanding of limits in higher dimensions
  • Explore online resources like Khan Academy or MIT OpenCourseWare for video tutorials on epsilon-delta proofs
  • Practice problems involving "Limits in Three Dimensions" to apply concepts learned
USEFUL FOR

Students studying calculus, particularly those focusing on multivariable functions, educators teaching epsilon-delta proofs, and anyone looking to strengthen their understanding of limits in three-dimensional contexts.

georgeh
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I am trying to show that a certain function, f(x) has a limit that approaches 1. Does anyone have any sites i can look at for epsilon delta proof for 3-space? I've saw the ones for two space, but they aren't really helping me out in this pickle..
thanks.
 
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What's the problem? What have you tried?
 
I think this is the one you're looking for.

[tex]\lim_{(x,y)\rightarrow(x_0,y_0)}f(x,y)=L[/tex] if for each [itex]\epsilon[/itex]>0 there corresponds a [itex]\delta[/itex]>0 such that [tex]|f(x,y)-L|<\epsilon[/tex] whenever [tex]0<\sqrt{(x-x_0)^2+(y-y_0)^2}<\delta[/tex].
 

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