8. Multiple Cholce 1 point Determine if L'Hopital's Rule can be used. If it can, solve the limit. If it cannot choose the appropriate response. \( \lim _{x \rightarrow 1} \frac{\ln x}{x-1} \) L'Hopital's Rule does not apply. (1) Previous

We first check if the limit is in an indeterminate form. As x approaches 1, the numerator ln(x) tends to ln(1) = 0 and the denominator x - 1 tends to 0. Since both numerator and denominator approach 0, we have a 0/0 indeterminate form, meaning L'Hôpital's Rule can be used. Applying L'Hôpital's Rule, we differentiate the numerator and denominator: • Derivative of ln(x) is 1/x. • Derivative of (x - 1) is 1. So, the limit becomes:   limₓ→₁ (1/x) = 1/1 = 1 Thus, the limit is 1.