Graphical Limits

Graphical limits are limits taken from a graph. They are helpful for functions with a point discontinuity. The need for defining limits of a function and the procedure to be carried out while determining the limit of a function can be easily understood by graphing a function. If you cannot determine the limit of a function algebraically, the graphical method is a good alternative.

Evaluate \(\displaystyle \lim_{x\to7}{\frac{x^2 - 49}{x - 7}}\).

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Graph \(\frac{x^2 - 49}{x - 7}\).

\(\frac{x^2 - 49}{x - 7}\)

At \(x = 7\) the graph shows the \(y\)-value as 14, even though there is a hole in the graph.

Therefore, \(\lim_{x\to7}{\frac{x^2 - 49}{x - 7}} = 14\). \( _\square \)