Infinite Limits — Question 5

Question 5 - Solution

We are given: $$\lim_{x \to 0^-} \frac{1}{x^2}$$

Step 1: Analyze the expression

As $x \to 0^-$, $x$ is approaching 0 from the left. So $x$ is negative, but very close to 0.

Now, consider the square of $x$: $$x^2 > 0 \text{ for all } x \neq 0$$

Even though $x$ is negative, $x^2$ is positive. As $x \to 0^-$, $x^2 \to 0^+$

Step 2: Behavior of the expression

$$\frac{1}{x^2} \to \frac{1}{\text{small positive number}} \to \infty$$

Conclusion: $$\boxed{\lim_{x \to 0^-} \frac{1}{x^2} = \infty}$$