Question

The value of \( \lim_{x \to 1} \frac{x^2 + 2x - 3}{x - 1} \) is:

• A. 2
• B. 4
• C. 3
• D. 1
• E. 0

Hint:

When encountering a limit with a factorable numerator, factor and cancel common terms to simplify.

Answer 1

The Correct Option is B

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: \[ \lim_{x \to 1} (x + 3) = 1 + 3 = 4 \]