Limits & Continuity

What does the limit of a function describe?

The value a function approaches as the input (x) gets closer and closer to a certain point

What is the standard notation for 'the limit of f(x) as x approaches a'?

lim(x→a) f(x)

Evaluate: lim(x→2) (x + 3)

5

What are the three conditions for a function to be continuous at a point x = a?

f(a) must be defined, the limit as x approaches a must exist, and the limit must equal f(a)

What is a common type of discontinuity where there is a single 'hole' in the graph?

A removable discontinuity