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Example:Finding Limit

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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 real-valued 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

 

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.