Computing Limits — Question 6

Question 6

Evaluate the limit: $$\lim_{x \to 1} \frac{x^2 - 1}{x - 1}$$

Question 6 - Solution

We are asked to evaluate: $$\lim_{x \to 1} \frac{x^2 - 1}{x - 1}$$

Step 1: Factor the numerator

Recall that $x^2 - 1 = (x - 1)(x + 1)$. So, $$\frac{x^2 - 1}{x - 1} = \frac{(x - 1)(x + 1)}{x - 1}$$

For $x \ne 1$, we can cancel $x - 1$ from numerator and denominator: $$= x + 1$$

Step 2: Take the limit

Now that the expression simplifies to $x + 1$, we compute: $$\lim_{x \to 1} (x + 1) = 2$$

Answer: $\boxed{2}$