Infinite limits occur when a function's value increases or decreases without bound as it approaches a certain point.
This often indicates a vertical asymptote at that point.
The cognitive trap here is thinking that infinite limits mean the function 'reaches' infinity.
It doesn't.
The function's value just grows larger or smaller indefinitely.
The mechanism is straightforward: if the limit of f(x) as x approaches c is infinity or negative infinity, there's likely a vertical asymptote at x = c.
Often, you see this in rational functions where the denominator approaches zero.
You might think direct substitution will work, but it doesn't.
Instead, you need to analyze the behavior of the function as x gets closer to the critical point.
Remember: it's not about finding a value but understanding the trend.
Misunderstanding this can cost you points because the AP expects you to articulate the behavior accurately, not just calculate blindly.
The challenge is maintaining precision in language and logic when the numbers themselves become unbounded.