Final answer:
The exponential function e^(-infinity) equals 0, and the exponential function e^(infinity) equals infinity.
Step-by-step explanation:
The exponential function e^(-infinity) equals 0, and the exponential function e^(infinity) equals infinity.
To understand this, let's look at the definition of the exponential function. The number e, approximately equal to 2.71828, is the base of the natural logarithm.
When a positive number is raised to infinity, it becomes infinitely large. That's why e^(infinity) equals infinity. On the other hand, when a positive number is raised to negative infinity, it approaches zero. Therefore, e^(-infinity) equals 0.