6.118 lim _(xarrow infty )((2x^3-3x^2+x+1)/(2x^3)-3x^(2-2x+3))^5x^(2)

To evaluate the limit , we can use the following steps:1. Divide both the numerator and denominator by , the highest power of in the denominator: 2. As approaches infinity, the terms with negative powers of will approach 0: 3. Simplify the expression: 4. Since any number raised to the power of infinity is 1: Therefore, the correct answer is 1.