The value of e raised to the power of negative infinity, denoted as e−∞
can be understood through the properties of exponential functions and limits.
The number e (approximately 2.718) is the base of natural logarithms and is a fundamental constant in mathematics. When you raise e to any negative power, the result is a fraction. For example,e−1 is 1/e, e−2 is 1/e2, and so on. As the negative exponent increases in magnitude (i.e., goes towards negative infinity), the fraction becomes smaller and smaller. In mathematical terms, as the exponent approaches negative infinity, the value of e raised to that exponent approaches zero. Therefore,
e−∞ is effectively 0. This is because you’re dividing 1 by an increasingly large number, which results in a value that gets closer and closer to zero but never actually reaches it. This concept is a fundamental aspect of limits in calculus.