Chapter 3 Review

Front

What is the definition of continuity in a function?

Back

A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point.

Front

What is a removable discontinuity?

Back

A removable discontinuity occurs when a function is not defined at a point, but can be made continuous by defining or redefining the function at that point.

Front

What is a jump discontinuity?

Back

A jump discontinuity occurs when the left-hand limit and right-hand limit of a function at a point exist but are not equal.

Front

What is an infinite discontinuity?

Back

An infinite discontinuity occurs when the function approaches infinity or negative infinity as it approaches a certain point.

Front

What does DNE stand for in the context of limits?

Back

DNE stands for 'Does Not Exist', indicating that a limit does not approach a finite value.

Front

What is the interval of continuity for the function f(x) = 1/(x+2)?

Back

The function is continuous for x in (-∞,-2)u(-2,∞).

Front

How do you determine if a function is continuous at a point?

Back

Check if the function is defined at that point, if the limit exists, and if the limit equals the function's value.

Front

What is the significance of one-sided limits?

Back

One-sided limits help determine the behavior of a function as it approaches a point from the left or right.

Front

What is the difference between a removable and non-removable discontinuity?

Back

A removable discontinuity can be 'fixed' by redefining the function at that point, while a non-removable discontinuity cannot.

Front

Provide an example of a function with a jump discontinuity.

Back

The piecewise function f(x) = { 1 for x < 0, 2 for x ≥ 0 } has a jump discontinuity at x = 0.