60–81. Limits Evaluate the following limits. Use l’Hôpital’s Rule when needed. 
lim_x→∞ (1 - (3/x))ˣ

Verified step by step guidance

1. Identify the limit to evaluate: lim_{x→∞} (1 - (3/x))^x.
2. Recognize that as x approaches infinity, (3/x) approaches 0, so the expression inside the limit approaches 1.
3. Rewrite the limit in a form suitable for l'Hôpital's Rule by taking the natural logarithm: let y = (1 - (3/x))^x, then ln(y) = x * ln(1 - (3/x)).
4. Evaluate the limit of ln(y) as x approaches infinity: lim_{x→∞} x * ln(1 - (3/x)). This is an indeterminate form of type ∞ * 0.
5. Apply l'Hôpital's Rule by rewriting the limit as a fraction: lim_{x→∞} ln(1 - (3/x)) / (1/x) and differentiate the numerator and denominator.