Per 1 Limits Graphically & Piecewise

Front

What is a limit in calculus?

Back

A limit is a value that a function approaches as the input approaches some value.

Front

What does it mean for a limit to exist?

Back

A limit exists if the function approaches the same value from both the left and right sides as the input approaches a certain point.

Front

What is a one-sided limit?

Back

A one-sided limit is the value that a function approaches as the input approaches a certain point from one side only (either left or right).

Front

How do you denote the limit of f(x) as x approaches a from the left?

Back

It is denoted as lim (x -> a-) f(x).

Front

How do you denote the limit of f(x) as x approaches a from the right?

Back

It is denoted as lim (x -> a+) f(x).

Front

What is the limit of f(x) as x approaches 1 from the right if f(x) = { -2 for x > 1 }?

Back

The limit is -2.

Front

What is the limit of f(x) as x approaches 1 from the left if f(x) = { 4 for x < 1 }?

Back

The limit is 4.

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 specific value.

Front

What is a piecewise function?

Back

A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the domain.

Front

How do you find the limit of a piecewise function?

Back

Evaluate the limit from both sides at the point of interest and check if they are equal.