Limits are a very powerful tool in mathematics and are used throughout calculus and beyond. The key idea is that a limit is what I like to call a \behavior operator". A limit will tell you the …

Limit Theorems Basic Properties of Limits - Let f : A n m and g : A n m with x0 A or a −→ R ⊂ R −→ R ∈ boundary point of A. If lim f(x) = b1 and lim g(x) = b2, then

There are a many better (and more accurate) ways to find the value of the limit than graphing or plugging in numbers that get closer and closer to the value of interest.

Limit Laws Stewart x1.6 erations on limits. Some general combination rules make most limit c mputations routine. Suppose we know that limx!a f(x) an limx!a g(x) exist. Then we

The good thing about this de nition is that it de nes the limit in terms of the ordinary ideas of subtracting numbers and comparing them with <. It gets rid of the vague and imprecise idea of …

Solution: Applying the limit law for products (provisionally), lim (f(x)g(x)) = lim f(x) x!2 x!2 lim g(x)

Each can be proven using a formal definition of a limit. We list some of them, usually both using mathematical notation and using plain language. It is the plain language that should be remem …