Limits by Graph and Table

Front

What is a limit in calculus?

Back

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

Front

What does it mean if a limit does not exist (DNE)?

Back

It means that the function does not approach a specific value as the input approaches a certain point.

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow3}f(x) = ?@@

Back

3

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow0}f(x) = ?@@

Back

DNE

Front

What is the limit of a function as x approaches a number from the left?

Back

It is the value that the function approaches as x gets closer to that number from the left side.

Front

Evaluate the limit: What is @@ ext{lim}_{x ightarrow0}f(x)@@ if f(x) approaches 5?

Back

5

Front

Evaluate the limit: What is @@ ext{lim}_{x ightarrow-4}f(x)@@ if f(x) approaches 2 from the left?

Back

2

Front

What is the significance of limits in calculus?

Back

Limits are fundamental in defining derivatives and integrals.

Front

What does it mean for a function to be continuous at a point?

Back

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

Front

What is the limit of a constant function?

Back

The limit of a constant function is the constant itself, regardless of the input.