Step 1 :Step 1: Divide each term in the function by \(x^2\), the highest power of x in the denominator. The function becomes \(\frac{4 - \frac{2}{x} + \frac{1}{x^2}}{6 + \frac{3}{x} - \frac{2}{x^2}}\)
Step 2 :Step 2: As x approaches infinity, the terms with x in the denominator tend to 0. So, the function simplifies to \(\frac{4}{6}\)
Step 3 :Step 3: Simplify the fraction to get the limit