Limieten numeriek en grafisch bepalen

Limits describe the value a system approaches as inputs change, even when the exact value is undefined or difficult to calculate. A variation of output and input values shows that as x nears 1, the output approaches 0.5.

Vehicle movement on a road illustrates this concept well. Light traffic allows smooth, high-speed travel.

As more vehicles enter the road, congestion increases, and average speed begins to drop.

At high densities, speed continues to decline and gets very close to zero.

This models a limit—speed approaching zero, representing gridlock, even if it never actually reaches zero.

This relationship is described by the formula: speed equals 100 times the natural logarithm of 200 divided by density.

Numerical data show that initially, increasing vehicle density causes noticeable speed reductions, though each added vehicle has a small effect.

Beyond a certain point, each added vehicle causes a larger drop in speed, quickly approaching gridlock.

A graph of speed versus vehicle density shows a downward-sloping curve that flattens near zero.

This curve visually represents a limit—speed approaches zero, but never quite reaches it.