[DRAFT] Limit

lim(f(x)) = L where x->a means, f(x) can be made as close to L as desired if x is close enough to a.

The limit of a sum is the sum of the limits, provided the limits exist. lim(f(x) + g(x)) = lim(f(x)) + lim(g(x))

lim(sin(1 / x)) where x->0 does not exist but

lim(sin(x) / x) where x->0 is 1 because of the Squeeze Theorem

The limit of the products is the product of the limits, provided the limits exist. lim(f(x) * g(x)) = lim(f(x)) * lim(g(x))

The limit of the quotient is the quotient of the limits, provided the limits exist and the denominator is not 0. lim(f(x) / g(x)) = lim(f(x)) / lim(g(x)), lim(g(x)) != 0

For one sided limits x->a+ means a right sided limit and x->a- means a left sided limit.

"f(x) is continuous at a" means lim(f(x)) = f(a) where x->a. Continiuty means nearby inputs are mapped to nearby outputs. Imagine a continious curve for example. Also check Intermediate Value Theorem.

Based on Intermediate Value Theorem, there is an 'x' so that f(x) = x. Imagine a map of Stockholm and there is a point on that map that is actually the point in the real world, that's the 'x'.