To find the limit of this expression as x approaches a certain value, you need to find the limit of each term in the expression.
As x approaches infinity, the terms that have the highest degree in the denominator will dominate the expression. In this case, the highest degree term in the denominator is 5x^3.
So the limit as x approaches infinity of (10x^2 + 2x - 8) / (5x^3 + 2x^2 + 2) is 0, because the degree of the denominator is higher than the degree of the numerator.
To simplify the expression, first multiply the terms in the numerator:
(5x - 4)(2x + 2) = 10x^2 + 10x - 8x - 8 = 10x^2 + 2x - 8
Now divide the numerator by the denominator:
(10x^2 + 2x - 8) / (5x^3 + 2x^2 + 2)
To find the limit of this expression as x approaches a certain value, you need to find the limit of each term in the expression.
As x approaches infinity, the terms that have the highest degree in the denominator will dominate the expression. In this case, the highest degree term in the denominator is 5x^3.
So the limit as x approaches infinity of (10x^2 + 2x - 8) / (5x^3 + 2x^2 + 2) is 0, because the degree of the denominator is higher than the degree of the numerator.