HI,
How would I go about proving that two limits are equal to each other using the Epsilon-Delta definition?
Moreover how can I prove that:
Why do I need to assume that δ=δ0?
How would I go about proving that two limits are equal to each other using the Epsilon-Delta definition?
Moreover how can I prove that:
[FONT=MathJax_Main]lim[FONT=MathJax_Math-italic]x[FONT=MathJax_Main]→[FONT=MathJax_Main]0[FONT=MathJax_Math-italic]f[FONT=MathJax_Main]([FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]lim[FONT=MathJax_Math-italic]x[FONT=MathJax_Main]→[FONT=MathJax_Math-italic]a[/FONT][/FONT][/FONT][/FONT][FONT=MathJax_Math-italic]f[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math-italic]a[/FONT][FONT=MathJax_Main])[/FONT][/FONT][/FONT][/FONT][/FONT]limx→0f(x)=limx→af(x−a)[/FONT][/FONT]
using the Epsilon-Delta definition? The intuition for this seem clear. However, I have do not know how a formal proof can be developed.Why do I need to assume that δ=δ0?