Explanation:
Limit (mathematics)
In mathematics, the concept of a
"limit" is used to describe the value that a function or sequence "approaches" as the
input or index approaches some value. Limits are essential to calculus (and mathematical analysis in general) and are used to
define continuity, derivatives, and integrals.
Limit
of a function
Suppose f(x) is a realvalued function and c is a real number. The expression
means that f(x) can
be made to be as close to L as desired by making x sufficiently
close to c. In that case, it can be stated that "the limit of f of x, as x approaches c, is L".
Note that this statement can be true even if f(c)
≠ L. Indeed, the function f(x) need
not even be defined at c.
For example, if
then f(1) is not defined (see Division by zero), yet as x moved arbitrarily close to 1, f(x)correspondingly approaches 2:
f(0.9)

f(0.99)

f(0.999)

f(1.0)

f(1.001)

f(1.01)

f(1.1)

1.900

1.990

1.999

⇒
undef ⇐

2.001

2.010

2.100

Thus, f(x) can
be made arbitrarily close to the limit of 2 just by making x sufficiently
close to 1.
http://en.wikipedia.org/wiki/Limit_(mathematics)
Limits of extra interest
(Our solved example in mathguru.com uses this concept)
For 0 < x < π/2:
sin x < x <
tan x.
Dividing everything by sin(x) yields
http://en.wikipedia.org/wiki/Limit_of_a_function
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