The Handy Math Answer Book

What are leftand right limits?

When a function is not defined around the point c(see the notation in the equation

above), but only to the left or right of point c,then the limits are called the left limit

and right limit at c. The formal left- and right-limit equations are the same as the

usual limit equation, except below the “lim” sign, the x$cis written as x$cfor

the left limit and x$cfor the right limit.

How is infinity treatedwhen discussing limits?

Defining infinity is a definite part of calculus, especially when discussing limits and

“negative” and “positive” infinity. Whenever the inverse of a small number is taken, a

large number is generated, and vice versa. In calculus, this is written as:

1/0 ±

But ±are no ordinary numbers, because they do not obey the usual rules of

arithmetic, such as  1 ;  1 ; 2 ; and so on. Therefore, in calcu-

lus functions, and thus limits, infinity is treated much differently. For example, for the

function f(x) 1 / x3, when x$3, then x 3 $0. The limit function then

becomes:

3

limfx() 01

"

==- - 3
x
218

Graph of an equation with infinity limited by x 3.