I've decided to teach myself calculus, I have a fairly solid

He's just giving you an example of how the limit can be visualized and rationalized. If you were to have a function y = x/sin(x), at x=0 the function is not defined (because we cannot divide by zero). Knowing this we have to use something called a limit. It just shows as a value approaches a point, the function in question converges to another point.

If you draw the graph you can see that it looks normal (it will even look like it passes through (0,1) ), but we still cannot define it for x=0. Graph the function and it might make more sense.

tl;dr - The picture is just giving an example of a limit, which you can think of as a fancy way of giving undefined points of a function legitimate values.

>>7778063
Google squeeze theorem.

>>7778063
ocw.mit.edu / stewart if you're a baby / apostol or spivak if you're badass

>>7780094
this.

and this >>7780099

>>7780094
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