Infinite Limits — Question 4

Question 4

Evaluate the following limit: $$\lim_{x \to 1^+} \frac{5}{x - 1}$$

Question 4 - Solution

We are given: $$\lim_{x \to 1^+} \frac{5}{x - 1}$$

Step 1: Understand the behavior of the denominator

As $x \to 1^+$, we are approaching 1 from the right. This means $x - 1$ is a small positive number.

Step 2: Behavior of the whole expression

$$\frac{5}{x - 1} \to \frac{5}{\text{small positive number}} \to +\infty$$

Conclusion: $$\boxed{\lim_{x \to 1^+} \frac{5}{x - 1} = \infty}$$