1. The problem is to understand why the limit $$\lim_{x \to 0^+} e^{1-\infty}$$ equals 0 and not negative infinity. 2. Recall the properties of limits and exponentials: when the exponent tends to negative infinity, the exponential function tends to zero, because $$e^{-\infty} = 0$$. 3. Here, the expression inside the exponent is $$1 - \infty$$, which simplifies to $$-\infty$$. 4. Therefore, $$e^{1-\infty} = e^{-\infty} = 0$$. 5. The answer is not negative infinity because the exponential function $$e^x$$ is always positive for any real number $$x$$, and it never reaches negative values. 6. So, even if the exponent tends to negative infinity, the value of the function tends to zero, not negative infinity. Final answer: $$\lim_{x \to 0^+} e^{1-\infty} = 0$$.