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What is the notation for a limit?

$\lim_{x \to a} f(x) = L$

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What is the notation for a limit?

$\lim_{x \to a} f(x) = L$

What is the notation for a right-hand limit?

$\lim_{x \to a^+} f(x) = L$

What is the notation for a left-hand limit?

$\lim_{x \to a^-} f(x) = L$

What form indicates that direct substitution won't work?

$\frac{0}{0}$

What is a limit?

The value a function approaches as the input (x) gets closer to a specific value.

Define one-sided limit.

The value a function approaches as the input (x) gets closer to a specific value from either the left or the right.

What does $\lim_{x \to a^+} f(x) = L$ mean?

The limit of f(x) as x approaches 'a' from the right (values greater than 'a') is L.

What does $\lim_{x \to a^-} f(x) = L$ mean?

The limit of f(x) as x approaches 'a' from the left (values less than 'a') is L.

What is an indeterminate form?

An expression, like $\frac{0}{0}$ , where the limit cannot be determined by direct substitution.

What does it mean for x-values to be 'close' to a?

Numbers in close proximity to 'a' from both the left and right sides.

When does a limit exist?

A limit exists only if the left-hand and right-hand limits are equal.

What is direct substitution?

Evaluating a limit by plugging in the value that x approaches into the function.

What is a vertical asymptote?

A vertical line x = a where the function approaches infinity or negative infinity as x approaches a.

Define $f(x)$

A function that takes an input $x$ and returns an output

What does the Existence of a Limit Theorem state?

$\lim_{x \to a} f(x)$ exists if and only if $\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x)$ .