Understanding limits is really important for figuring out the area under a curve, but it can be tough for students studying AP Calculus AB.

Here are some key points to consider:

1. Seeing the Area: When students try to find the area under a curve, they often have a hard time picturing it. The idea that this area can be estimated by cutting it into smaller rectangles (called Riemann sums) can feel strange and hard to understand.

2. The Limit Process: Another challenge is moving from adding up finite sums to dealing with infinite limits. This involves making the width of those rectangles, called $\Delta x$, get smaller and smaller, getting close to zero.

   As students learn that the area $A$ under a curve $f(x)$ from point $a$ to point $b$ can be shown with this formula:

   $A = \lim_{n \to \infty} \sum_{i=1}^{n} f(x_i^*) \Delta x$

   they might struggle to understand what this limit really means and how it changes an approximate value into a precise one.

3. Breaking Down the Challenges: To help students get past these difficulties, teachers can use visual tools like graphs and software that show how limits work. Working together in groups and solving problems as a team can also help students get a better grasp of how limits show the idea of adding up area.

In short, while the idea of limits in finding the area under a curve can be tricky, with the right teaching methods, students can learn to handle these challenges successfully.