Finding limits from graphs

Front

What is the definition of a limit in calculus?

Back

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

Front

How do you denote the limit of a function f(x) as x approaches a value a?

Back

It is denoted as lim (x→a) f(x).

Front

What does it mean if lim (x→a) f(x) = L?

Back

It means that as x gets closer to a, the function f(x) gets closer to the value L.

Front

What is the limit of a constant function?

Back

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

Front

What is the limit of f(x) as x approaches a if f(x) is continuous at a?

Back

If f(x) is continuous at a, then lim (x→a) f(x) = f(a).

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 value from one side (left or right).

Front

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

Back

It is denoted as lim (x→a-) f(x).

Front

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

Back

It is denoted as lim (x→a+) f(x).

Front

What does it mean if the left-hand limit and right-hand limit are not equal?

Back

If the left-hand limit and right-hand limit are not equal, the limit of f(x) as x approaches a does not exist.

Front

What is the Squeeze Theorem?

Back

The Squeeze Theorem states that if f(x) is squeezed between g(x) and h(x) and both g(x) and h(x) approach L as x approaches a, then f(x) also approaches L.