Infinite Limits — Question 8

Question 8 - Solution

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

Step 1: Analyze the expression near $x = 2^+$

As $x$ approaches 2 from the right, the value of $x - 2$ becomes a very small positive number. Therefore, $\frac{1}{x - 2}$ becomes a very large positive number.

$$x \to 2^+ \quad \Rightarrow \quad x - 2 \to 0^+ \quad \Rightarrow \quad \frac{1}{x - 2} \to +\infty$$

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

This indicates that the function grows without bound as $x$ approaches 2 from the right.