Practice Demo

Find the limit if it exists. If the limit cannot be specified as a constant or infinity, enter $_DNE_$.
$$\lim_{z\to 4 }{\frac{-2}{20 - 9z+z^{2}}}$$

Preview your answer:

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Hint 1: We can graph the function $_\frac{-2}{20 - 9z+z^{2}}_$ to see what happens near $_z=4_$:

Solution:

From the graph, we can see that the left and right limits are different. Therefore,

$$\lim_{z\to 4 }{\frac{-2}{20 - 9z+z^{2}}} \text{ does not exist.} $$