- #1

- 172

- 0

**[SOLVED] Help Deciphering limit text**

"The function [tex]f(x) = 3x[/tex] aproaches the limit 6 as [tex]x\rightarrow 2[/tex]. In fact, given any [tex]\epsilon > 0 [/tex], choose [tex]\delta = \frac {\epsilon} {3}[/tex]. We then have

[tex]|f(x)-6|=|3x-6|=3|x-2|<3\delta = \epsilon[/tex] whenever [tex]0<|x-2|<\delta[/tex]."

How is the book allowed to set [tex]3|x-2|<3\delta[/tex](the 3 * delta), and better yet,

[tex]3|x-2|=\epsilon[/tex](= epsilon)? I thought the limit designated to them was delta alone, not 3 delta. In addition, how are they allowed to set it equal to epsilon?

I am really trying to understand this; I realize the answer to my questions may seem, "elementary", but I am trying to master the basics of Calculus(currently in pre-calculus).