Question:
The value of \( \lim_{x \to 1} \frac{x^2 + 2x - 3}{x - 1} \) is:
The value of \( \lim_{x \to 1} \frac{x^2 + 2x - 3}{x - 1} \) is:
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When encountering a limit with a factorable numerator, factor and cancel common terms to simplify.
Updated On: Mar 7, 2025
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The Correct Option is B
Solution and Explanation
We can simplify the expression:
\[
\lim_{x \to 1} \frac{x^2 + 2x - 3}{x - 1}
\]
Factor the numerator:
\[
\frac{x^2 + 2x - 3}{x - 1} = \frac{(x - 1)(x + 3)}{x - 1}
\]
Cancel out \( (x - 1) \) from the numerator and denominator:
\[
\lim_{x \to 1} (x + 3) = 1 + 3 = 4
\]
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