Word Count : 198

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Let's examine the limit: \[ \lim_{x \rightarrow 0} \frac{e^{1/x}}{e^{1/x} + 1} \] To solve this, we'll check the behavior of the function as \(x\) approaches 0 from both the left and the right. ### 1. As \(x \to 0^+\) (approaching from the right): As \(x \to 0^+\), \( \frac{1}{x} ___ ________ ____ _____ ___ _______.
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