Evaluate the Limit

Problem

(lim_x→−∞)(e^x)

Solution

1. Identify the behavior of the exponential function e^x 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→−∞)(e^x)=0

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