code: def limit_at_inf(num, den, x):
      """
      Find the limit of a rational function
      at oo
      """
      # pwr = degree(num) - degree(den)
      pwr = -val_at_inf(num, den, x)
      # Numerator has a greater degree than denominator
      # Limit at infinity would depend on the sign of the
      # leading coefficients of numerator and denominator
      if pwr > 0:
          return oo * sign(num.LC() / den.LC())
      # Degree of numerator is equal to that of denominator
      # Limit at infinity is just the ratio of leading coeffs
      elif pwr == 0:
          return num.LC() / den.LC()
      # Degree of numerator is less than that of denominator
      # Limit at infinity is just 0
      else:
          return 0
  
imports: from itertools import product
  from sympy.core import S
  from sympy.core.add import Add
  from sympy.core.numbers import oo, Float
  from sympy.core.function import count_ops
  from sympy.core.relational import Eq
  from sympy.core.symbol import symbols, Symbol, Dummy
  from sympy.functions import sqrt, exp
  from sympy.functions.elementary.complexes import sign
  from sympy.integrals.integrals import Integral
  from sympy.polys.domains import ZZ
  from sympy.polys.polytools import Poly
  from sympy.polys.polyroots import roots
  from sympy.solvers.solveset import linsolve
label_desc: Use image node_id 9 for calling a global function with example usage: limit_at_inf(num, den, x) and returns: unknown, unknown, int