6.115 . lim _(xarrow infty )((2x^2+3)/(2x^2)-4)^3x

To solve this limit, we can use the properties of exponents and the fact that the limit of a constant raised to infinity is 1.First, let's rewrite the expression inside the parentheses: Now, we can rewrite the original expression as: Next, we can use the property of exponents that states as approaches infinity: As approaches infinity, approaches 0, so the expression simplifies to: Therefore, the limit is .