1. The problem is to understand why $$e^{1 - \infty} = e^{-\infty} = 0$$ when evaluating the limit of a function as $x \to 0^+$. 2. Recall the properties of exponents and limits: when you have an expression like $e^a$, where $a$ tends to $-\infty$, the value of $e^a$ tends to zero because the exponential function decreases rapidly towards zero for large negative exponents. 3. In the expression $e^{1 - \infty}$, the term $1$ is finite, but subtracting infinity dominates, so $1 - \infty$ effectively behaves like $-\infty$. 4. Therefore, $e^{1 - \infty} = e^{-\infty}$. Since $e^{-\infty}$ means the exponential function with an exponent tending to negative infinity, the value approaches zero. 5. In simpler terms, as the exponent becomes very large in the negative direction, the exponential function's value gets closer and closer to zero, which explains why the limit is zero.