Questions: Find the one-sided limit. lim (x → 0^+) (x-5)/x

Solution Steps

We need to evaluate the one-sided limit \( \lim_{x \rightarrow 0^{+}} \left( \frac{x - 5}{x} \right) \). As \( x \) approaches 0 from the positive side, we can rewrite the expression as \( \frac{x}{x} - \frac{5}{x} \), which simplifies to \( 1 - \frac{5}{x} \).

As \( x \) approaches 0 from the right, the term \( \frac{5}{x} \) becomes very large and positive, leading the entire expression \( 1 - \frac{5}{x} \) to approach negative infinity. Therefore, we conclude that the limit diverges to negative infinity.

Final Answer