Evaluate \(\lim \limits_{x \to 3} \frac{x^{2} - 2x - 3}{x - 3}\)
Question 1 Report
Evaluate \(\lim \limits_{x \to 3} \frac{x^{2} - 2x - 3}{x - 3}\)
Answer Details
We can evaluate the given limit by plugging in the value 3 directly into the expression, but this results in a division by zero, which is undefined. Instead, we can use algebraic techniques to simplify the expression and evaluate the limit.
We can factor the numerator of the expression as follows:
\(x^{2} - 2x - 3 = (x - 3)(x + 1)\)
Substituting this factorization into the original expression, we get:
\(\frac{x^{2} - 2x - 3}{x - 3} = \frac{(x - 3)(x + 1)}{x - 3} = x + 1\)
Now, we can take the limit of the simplified expression as x approaches 3:
\(\lim \limits_{x \to 3} x + 1 = 3 + 1 = 4\)
Therefore, the value of the given limit is 4, which is the correct answer.
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