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Right- and left-handed limits : Next, let's see precise definitions for the right- & left-handed limits.
Definition For the right-hand limit we say that,
if for every number ε > 0 there is some number δ > 0 such that
|f ( x ) - L| < ε whenever 0 < x - a < δ or a < x Definition For the left-hand limit we say that, if in support of every number ε < 0 there is some number δ > 0 such that |f ( x ) - L |< ε whenever - δ < x - a < 0 or (a - δ < x < a ) Note as well that along with both of these definitions there are two ways to deal along with the limitation on x and the one in parenthesis is possibly the easier to use, though the main one given more nearly matches the definition of the normal limit above. Let's work a quick instance of one of these, even though as you'll see they work in much the similar manner as the normal limit problems do.
Definition For the left-hand limit we say that,
if in support of every number ε < 0 there is some number δ > 0 such that
|f ( x ) - L |< ε whenever - δ < x - a < 0 or (a - δ < x < a )
Note as well that along with both of these definitions there are two ways to deal along with the limitation on x and the one in parenthesis is possibly the easier to use, though the main one given more nearly matches the definition of the normal limit above.
Let's work a quick instance of one of these, even though as you'll see they work in much the similar manner as the normal limit problems do.
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