Evaluate the Limit limit as x approaches infinity of e^x

Problem

(lim_x→∞)(ex)

Solution

1. Identify the behavior of the base e which is a constant approximately equal to 2.718

2. Analyze the function ƒ(x)=ex as the exponent x increases without bound.

3. Determine that as x grows larger and larger, ex also grows larger and larger at an increasing rate.

4. Conclude that the function does not approach a finite value but instead approaches infinity.

Final Answer

(lim_x→∞)(ex)=∞

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