Simplify e^negative infinity

Problem

e(−∞)

Solution

1. Identify the expression as a limit of the exponential function as the exponent approaches negative infinity.

2. Apply the property of negative exponents to rewrite the expression as a fraction.

e(−∞)=1/(e∞)

3. Evaluate the behavior of the denominator, noting that as x grows without bound, ex also grows without bound.

e∞→∞

4. Determine the limit of the fraction, where a constant divided by an increasingly large number approaches zero.

1/∞→0

Final Answer

e(−∞)=0

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