Question

lim (х-8) / (2х-2) x→∞

Answer 1

$\lim_{x \to \infty} \frac{(x-8)}{(2x-2)} = \frac{1}{2}$

Answer 2

lim (x-8)/(2x-2) as x approaches infinity

To solve this limit, we can use the concept of asymptotes. As x approaches infinity, the terms with the highest power in the numerator and denominator dominate the expression. In this case, both x and 2x are the highest power terms in the numerator and denominator, respectively.

So, we can simplify the expression by dividing both the numerator and denominator by x:

lim (x-8)/(2x-2) = lim (1 - 8/x)/(2 - 2/x) as x approaches infinity

As x approaches infinity, the terms with 1/x in the denominator become negligible, so we can simplify further:

lim (1 - 8/x)/(2 - 2/x) = (1 - 0)/(2 - 0) = 1/2

Therefore, the limit of (x-8)/(2x-2) as x approaches infinity is 1/2.