Determine the infinite limit. lim x→8+ ln(x2 − 64) ∞−∞

The expression you've given seems to be a bit confusing. However, if you're asking for the limit as x approaches 8 from the right for the function ln(x^2 - 64), here's how you can solve it:

Step 1: Identify the function The function is f(x) = ln(x^2 - 64).

Step 2: Substitute the limit value into the function As x approaches 8 from the right, the expression inside the logarithm (x^2 - 64) becomes slightly greater than zero (because 8^2 - 64 = 0).

Step 3: Evaluate the limit The natural logarithm of a number slightly greater than zero is a very large negative number. Therefore, as x approaches 8 from the right, ln(x^2 - 64) approaches negative infinity.

So, the limit of the function as x approaches 8 from the right is negative infinity.