\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
For the polynomial \(P(x) = x^7 + 100x^6 - 500x^2\), determine the following limits:
  1. \(\displaystyle\lim_{x \to \infty} P(x) = \)
  2. \(\displaystyle\lim_{x \to -\infty} P(x) = \)