Evaluate the Limit limit as x approaches infinity of e^(-x)

Problem

(lim_x→∞)(e(−x))

Solution

1. Rewrite the expression using the property of negative exponents to make the behavior clearer.

(lim_x→∞)(1/(ex))

2. Analyze the behavior of the denominator as x grows without bound.

As *x→∞,ex→∞

3. Evaluate the limit by observing that a fraction with a constant numerator and a denominator that approaches infinity will approach zero.

1/∞→0

Final Answer

(lim_x→∞)(e(−x))=0

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