APFIVE Limit With a Removable Discontinuity
A researcher examines the function
$$ f(x) = \frac{2 * x^2 - 8}{x - 2} $$
as $$ x \to 2 $$ and, by directly substituting $$ x = 2 $$, concludes that the limit is infinite. What mistake did they make?
A
They misinterpreted the behavior of quadratic functions.
B
They incorrectly applied L’Hôpital’s rule.
C
They failed to factor and cancel the common factor $$ (x - 2) $$, ignoring the removable discontinuity.
D
They substituted into the wrong part of the function.
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