Visualization and interpretation of the limit

The limit is at a from the left The limit is at a from the left. The values of x approach a from the left. i.e. the values of x increase to a The values of f (x) increase without bound We present next, a possible graph of a function with this limit.

f (x) increases without bound as

This limit indicates that the line x = a is a vertical asymptote in the positive direction

An interpretation of this limit If p is the area contaminated by toxic waste and C is the cost of cleaning the area p, then the limit is interpreted as

The cost of cleaning the toxic waste increases without bound as the area p increases to L When that area reaches L the cost of cleaning it becomes unaffordable