Question

http://www.themathpage.com/acalc/limits-2.htm states:
1) The limit of a sum is equal to the sum of the limits.
2) The limit of a product is equal to the product of the limits.
3) The limit of a quotient is equal to the quotient of the limits,
3) provided the limit of the denominator is not 0.

Now... is limit a noun or a verb? I don't understand these rules. I can't picture it, it's an opaque operation (eg. rule #1)

Answer 1

Also, they freely say things like \[\lim_{x \rightarrow c} f(x) = c\] eg. if f(x) = x)
However, it's not really equal is it, because, c a limit, a boundary.

Answer 2

1) The limit of a sum is equal to the sum of the limits.
means
\[Lim_{x \rightarrow a} (x^2+x) = Lim_{x \rightarrow a} \ x^2 + Lim_{x \rightarrow a} \ x\]

Answer 3

Its like Lim is distributive over addition. I don't get it. Maybe when I use it I'll intuit..