Question:
Evaluate $ \lim_{x \to 2} \frac{x^2 - 4}{x - 2} $.
Evaluate $ \lim_{x \to 2} \frac{x^2 - 4}{x - 2} $.
Show Hint
For limits yielding \( \frac{0}{0} \), factorize or simplify the expression to cancel common terms, then evaluate the limit.
Updated On: May 25, 2025
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The Correct Option is C
Solution and Explanation
Evaluate the limit:
\[
\lim_{x \to 2} \frac{x^2 - 4}{x - 2}
\]
Since substituting \( x = 2 \) gives \( \frac{0}{0} \), factorize the numerator:
\[
x^2 - 4 = (x - 2)(x + 2)
\]
\[
\frac{x^2 - 4}{x - 2} = \frac{(x - 2)(x + 2)}{x - 2} = x + 2 \quad (x \neq 2)
\]
Now take the limit:
\[
\lim_{x \to 2} (x + 2) = 2 + 2 = 4
\]
Thus, the value of the limit is:
\[
\boxed{4}
\]
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