6.117. lim _(xarrow infty )((5x^3-2)/(5x^3)+1)^-6x^(3)

To solve this limit, we can use the properties of exponents and the fact that as approaches infinity, the dominant terms in the numerator and denominator will be the highest degree terms.First, let's rewrite the expression inside the limit: We can simplify the fraction inside the limit: As approaches infinity, the terms and approach 0. Therefore, the fraction simplifies to: So, the expression inside the limit becomes: Therefore, the limit is: Thus, the correct answer is: