SAO Maths Primer

The above equation can simply be expressed as follows " f(x) approaches L as x approaches a ".

Let's see some examples:

Example 1 This graphic shows the function   y = x2+2 What is the limit of the function as x approaches 0? This case is an easy one, obviously L=2 , which you can find just by substituting x=0 in the function.

But sometimes calculating limits is not that easy:

Example 2 This graphic shows the function   y=1/x . In this case you cannot find the limit as x approaches zero just by substituting x=0 into the function. What you have to do is to study the behaviour of the function as smaller and smaller values of x are given, and in this case it will be important whether x is a positive or a negative number:

When x is a small positive number y is a large positive number. The smaller x becomes the larger y is. When x is a small negative number y is a large negative number. The smaller x is the larger y (negative) becomes. Then in this case we say that the limit of the function as x approaches 0 through positive values is +infinity, and the limit of the function as x approaches 0 through negative values is -infinity. What about the limit of the function when x takes very large values (i.e. when x approaches infinity)? Following a similar procedure you can see that as x tends to infinity (either through positive or negative numbers) the function y tends to zero.

See also: function

Recommended Web Sites:

Eric Weisstein's world of Mathematics mathworld.wolfram.com

S.O.S. Mathematics www.sosmath.com

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