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"To define limits, let us recall that the distance between two numbers a and b is the absolute value of a - b, so we can express the idea that f(x) is close to L by saying that the absolute value of f(x) - L is small."

Why does this make no sense to me? What does subtracting a function say: f(x) = x^2-x-2 from L (which i assume (L) means the limit of a function) have to do with a limit of a function. Does it have something to do with the limit of the function that we subtracted the limit of that function from.. I just do not get it!!!!

So, the lim as x approaches c of f(x) = L

what does L stand for... does it stand for the actual number c or does it stand for some abstract concept about taking the limit of c? What does c stand for, and for that matter does f(x) still mean the y axis??... Am I suppose to be thinking of two different graphs here???? I am so confused.

I failed my first calc test... this is the first time in my life I have failed a math test... I studied, I always study but they confused the crap out of me there was no actual math it was all this conceptual ways of thinking about the notations of limits....

For instance:

Assume that: the lim as x approaches infinity of f(x) = L and the lim as x approaches L of g(x) = infinity,

true/false:

A) x = L is a vertical asymptote of g(x).

B) y = L is a horizontal asymptote of g(x).

C) x = L is a vertical asymptote of f(x).

D) y = L is a horizontal asymptote of f(x).

My book mentioned one thing about asymptote's and that is this rule: "A horizontal line y = L is a horizontal asymptote if: the lim as x goes to infinity of f(x) = L and/or the lim as x goes to negative infinity of f(x) = L"

Guess which one of those questions i got right... is this some new thing about math in calculus I now have to be able to manipulate the books words and notations in order to figure this stuff out all on my own....? I mean didn't it takes thousands of years before one or two guys figured this out on there own?????? They expect us all to be as good at math as Newton or am I just completely missing something about limits and the manipulation of theorems. Maybe I just have no imagination and so I can go no further in math....???

I know this is a lot and I don't expect someone to answer all of my questions but I will take any help on translating this notional crap that's in my book into something useful that I can actually work with and understand.