Numerical methods are helpful for figuring out limits in calculus for a few important reasons:

1. Table Method: By making a table of values near the point we're looking at, we can see how the function behaves.

   • For example, if we look at the function ( f(x) = \frac{x^2 - 4}{x - 2} ) close to ( x = 2 ), we can check the values of ( f(1.9) ), ( f(1.95) ), ( f(2.05) ), and ( f(2.1) ).

2. Graphical Analysis: Drawing graphs of functions helps us notice patterns as ( x ) gets closer to a limit.

   • Research shows that about 70% of students find it easier to understand when they see graphical displays.

3. Approximation Techniques: Using numbers that are really close to the limit point helps us get more precise answers.

   • For example, examining limits at tiny decimal changes, like ( 0.1 ) increments, can make things clearer.