The condition of continuity is expressed in terms of limit and function value. Both of these are required to exist and be equal. We shall learn about these aspects more in detail after having brief overview of these terms.

** Limit from left **

The limit from left means that a function approaches a value (

We show here three illustrations of “limit from left”. The important aspect of these figures is that graph tends to a particular value (infinity is also included). This is done by showing the orientation of graph pointing to limiting value when x is infinitesimally close to test point. Important point to note is that graph does not reach limiting value. Note empty circle at the end of graph, which represents the value of limit not yet occupied by graph. Similarly, asymptotic nature of graph tending to infinity maintains a small distance away from asymptotes, denoting that graph does not reach limiting value.

Limit from left |
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** Limit from right **

The limit from right means that a function approaches a value (

We show here three illustrations of “limit from right" as in the earlier case. Important point to note is that graph does not reach limiting value, which represents the value of limit not yet occupied by graph.

Limit from right |
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** Limit at a point **

The limit at a point means that a function approaches a value (L) as x approaches the test point “a” from either side.

We show here three illustrations of limit at a point. Important point to again note is that graph does not reach limiting value, which represents the value of limit not yet occupied by graph.

Limit at a point |
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** Function value **

Function value is obtained by substituting x values in the function. In case of rational function, we first reduce expression by removing common factors from numerator and denominator.