AP Calculus AB Practice Limits (1.2 - 1.3)

Front

What is a limit in calculus?

Back

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

Front

Define the notation \( \lim_{x \to c} f(x) \).

Back

It represents the limit of the function \( f(x) \) as \( x \) approaches the value \( c \).

Front

What does it mean if \( \lim_{x \to c} f(x) = DNE \)?

Back

It means that the limit does not exist; the function does not approach a specific value as \( x \) approaches \( c \).

Front

How do you find \( \lim_{x \to c^-} f(x) \)?

Back

Evaluate the limit of \( f(x) \) as \( x \) approaches \( c \) from the left side.

Front

How do you find \( \lim_{x \to c^+} f(x) \)?

Back

Evaluate the limit of \( f(x) \) as \( x \) approaches \( c \) from the right side.

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 \( f(x) = \frac{1}{x} \) as \( x \to 0 \)?

Back

The limit does not exist (DNE) because the function approaches \( \infty \) from the right and \( -\infty \) from the left.

Front

If \( f(x) \) is continuous at \( c \), what is \( \lim_{x \to c} f(x) \)?

Back

If \( f(x) \) is continuous at \( c \), then \( \lim_{x \to c} f(x) = f(c) \).

Front

What is the Squeeze Theorem?

Back

If \( g(x) \leq f(x) \leq h(x) \) and \( \lim_{x \to c} g(x) = \lim_{x \to c} h(x) = L \), then \( \lim_{x \to c} f(x) = L \).

Front

What is the limit of \( f(x) = x^2 \) as \( x \to 3 \)?

Back

The limit is \( 9 \) because \( f(3) = 3^2 = 9 \).