Answer: The value of e^(-∞) (e to the power of negative infinity) is equal to zero.
To see why, recall that e is a positive constant approximately equal to 2.71828. As the exponent approaches negative infinity, e^(-∞) represents the limit of a number getting closer and closer to zero but never actually reaching zero.
We can use the limit definition to evaluate the limit of e^(-x) as x approaches infinity:
lim e^(-x) = 0
x→∞
To see this, note that as x becomes very large, the denominator e^x becomes very large, causing the fraction to approach zero. Since the limit of e^(-x) as x approaches infinity is zero, we can say that e^(-∞) is also equal to zero.
In summary, e^(-∞) = 0.
Explanation: