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Analysis and Calculus
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What is the limit of the function (f(x) = \frac{x^2 - 4}{x - 2}) as (x) approaches (2)?
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A
4
💡 Explanation:
We can use L'Hopital's rule to evaluate the limit. Taking the derivative of the numerator and denominator, we get (f'(x) = \frac{2x}{1} = 2x) and (g'(x) = \frac{1}{1} = 1). Substituting (x = 2), we get (f'(2) = 4) and (g'(2) = 1). Therefore, the limit of (f(x)) as (x) approaches (2) is (\frac{4}{1} = 4).