Graphical Limits

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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 $\displaystyle \lim_{x\to7}{\frac{x^2 - 49}{x - 7}}$.

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

$\frac{x^2 - 49}{x - 7}$ $\frac{x^2 - 49}{x - 7}$

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 $