Infinite Limits — Question 3

Question 3 - Solution

We are given: $$\lim_{x \to 3^-} \frac{1}{(x - 3)^2}$$

Step 1: Analyze the behavior of the denominator

As $x \to 3^-$, we are approaching 3 from the left. The expression $x - 3$ becomes a small negative number. But since it is squared: $$(x - 3)^2 \to 0^+ \quad \text{(very small positive number)}$$

Step 2: Behavior of the function

Since we are dividing by a very small positive number, the entire expression becomes very large: $$\frac{1}{(x - 3)^2} \to +\infty$$

Conclusion: $$\boxed{\lim_{x \to 3^-} \frac{1}{(x - 3)^2} = \infty}$$