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ok

the example my textbook gives is the following:
"Show that the \(\lim_{x\rightarrow1}(5x-3)=2\)"

Then, they use substitutions with what is given
c=1,L=2.

So we show this statement to be true? \(0<|x-1|<\delta \rightarrow|f(x)-2|<\epsilon\)

and \[\epsilon\to0\]

as \(x\to1\), \(\delta\to0\implies\epsilon\to0\)

so they essentially manipulate the f(x)-L expression to arrive at the x-c expression?

that would be backward mapping... map "f(x)" to "x" given "L"

called image

it is very similar to the process of obtaining the vertical asymptote of a function.

What I don' get is the last part.
"thus we can take \(\delta=\epsilon/5\) If 0<|x-1|

ooooh

I do not understand the last question

no, they are not. they are "rational" functions

you can play with rational numbers as long as you avoid "divisions with "0""

surething

xD was it the integral of sqrt(tan x) by any chance?

dont remember exactly.. it was a form of Beta function

oh wow... I got a while before I'll even remotely understand that...

i htink i was\[\int_0^1\frac{\mathrm{d}x}{\sqrt{1-x^m}}\]