Limit With a Removable Discontinuity

Question

When evaluating the limit of the function $$ f(x) = \frac{2x^2 - 8}{x - 2} $$ as $$ x 	o 2 $$, a student directly substitutes $$ x = 2 $$ and concludes that the limit is infinite. What is the error in this reasoning?

Accepted Answer

They failed to factor and cancel the common factor $$ (x - 2) $$, ignoring the removable discontinuity.

Answer

They substituted into the wrong part of the function.

Answer

They misinterpreted the behavior of quadratic functions.

Answer

They incorrectly applied L'Hôpital's rule.

Limit With a Removable Discontinuity

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