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Let \(f\) be the function defined on \((0, +\infty)\) by:$$ f(x) = \ln(x+1) - \ln(x) $$
  1. Justify that direct evaluation of the limit at \(+\infty\) leads to an indeterminate form.
  2. Use the properties of logarithms to show that \(f(x) = \ln\left(1 + \dfrac{1}{x}\right)\).
  3. Evaluate \(\displaystyle\lim_{x \to +\infty} f(x)\) and state the equation of the horizontal asymptote.

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