Question

What is the value of e^infinity and e^-infinity

Answer 1

In mathematics, the value of e^infinity is considered to be infinity, reflecting unbounded growth, while e^-infinity represents an exponential decay towards zero.

Step-by-step explanation:

When evaluating the expressions e^infinity and e^-infinity, we are considering the behavior of the exponential function at the extremes. The value of e, approximately equal to 2.71828, when raised to the power of infinity, grows without bound, and hence e^infinity is considered to be infinity. This represents a situation where a quantity is increasing exponentially without any upper limit.

Conversely, e^-infinity describes an exponential decay towards zero as the power of e is negative and approaching infinity. Thus, the value of e^-infinity is zero, representing a quantity that has decreased exponentially and virtually vanished. These considerations are central in various physical contexts, such as the electric potential around charges or in radioactive decay, where exponential functions often arise.

These insights help to evaluate the reasonableness of answers in physics by considering extreme cases (e.g., when the distance approaches infinity) and ensuring that the resultant expressions align with physical expectations—such as potentials becoming zero at infinity or fields decreasing with certain power-law dependencies.

Answer 2

e^(∞): This is defined as 'e' being raised to a huge value. Hence the result will definitely be a large number which is also infinity (∞), i.e. e^(∞) = ∞. e^(- ∞) = 1/e^(∞) = 1/∞ = 0.