code: def main():
      x = Symbol("x")
  
      show(limit(sqrt(x**2 - 5 * x + 6) - x, x, oo), -Rational(5) / 2)
  
      show(limit(x * (sqrt(x**2 + 1) - x), x, oo), Rational(1) / 2)
  
      show(limit(x - sqrt3(x**3 - 1), x, oo), Rational(0))
  
      show(limit(log(1 + exp(x)) / x, x, -oo), Rational(0))
  
      show(limit(log(1 + exp(x)) / x, x, oo), Rational(1))
  
      show(limit(sin(3 * x) / x, x, 0), Rational(3))
  
      show(limit(sin(5 * x) / sin(2 * x), x, 0), Rational(5) / 2)
  
      show(limit(((x - 1) / (x + 1)) ** x, x, oo), exp(-2))
  
imports: from sympy import exp, log, Symbol, Rational, sin, limit, sqrt, oo
label_desc: Use image node_id 3 for calling a global function with example usage: main() without return types