Evaluate the Limit

Problem

(lim_x→−∞)(ex)

Solution

1. Identify the behavior of the exponential function ex as the exponent x decreases without bound toward negative infinity.

2. Rewrite the expression using the property of negative exponents, e(−|x|)=1/(e|x|) to visualize the limit as x→−∞

3. Analyze the denominator as x→−∞ noting that e|x| grows infinitely large.

4. Determine that a fraction with a constant numerator and a denominator that approaches infinity results in a limit of 0

Final Answer

(lim_x→−∞)(ex)=0

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