Final answer:
When evaluating 25/sqrt(x²-1) as x approaches negative infinity, the denominator becomes very large, resulting in the expression approaching 0.
Step-by-step explanation:
To evaluate 25/sqrt(x²-1) as x approaches negative infinity, we need to look at the behavior of the function as x becomes a very large negative number. Since x² grows faster than x, as x becomes more negative, x² becomes very large, making the square root of (x²-1) almost equal to the square root of x², which is |x|. So, our expression simplifies to 25/|x| as x approaches negative infinity.
Since we are dealing with negative infinity, |x| will be a very large positive number. Therefore, 25/|x| will approach zero. Thus, the value of the original expression as x approaches negative infinity is 0.