1. The problem is to understand how to handle the limit definition when the limit $L = -\infty$. 2. The standard limit definition for a finite limit $L$ is: for every $\epsilon > 0$, there exists a $\delta > 0$ such that if $0 < |x - a| < \delta$, then $|f(x) - L| < \epsilon$. 3. However, when $L = -\infty$, the definition changes because $|f(x) - L|$ is not meaningful (distance to $-\infty$ is not finite). 4. The correct definition for $\lim_{x \to a} f(x) = -\infty$ is: for every $M < 0$ (a large negative number), there exists a $\delta > 0$ such that if $0 < |x - a| < \delta$, then $f(x) < M$. 5. This means the function values become arbitrarily large in the negative direction as $x$ approaches $a$. 6. So, instead of using $|f(x) - L| < \epsilon$, we use $f(x) < M$ for any negative $M$ to handle limits going to $-\infty$. This is how you handle the limit definition when $L = -\infty$.