Direct Substitution: Simple, but fails for indeterminate forms. | Tables: Useful for indeterminate forms, but requires more computation and careful observation.

Left-hand Limit: Approaching from values less than 'a'. | Right-hand Limit: Approaching from values greater than 'a'.

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

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

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

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

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

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

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

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

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

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

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