The value that a function approaches as the input approaches some value.

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

An expression whose value cannot be determined, such as 0/0.

The limit of a sum is the sum of the limits: $lim_{x o c} [f(x) + g(x)] = lim_{x o c} f(x) + lim_{x o c} g(x)$

The limit of a difference is the difference of the limits: $lim_{x o c} [f(x) - g(x)] = lim_{x o c} f(x) - lim_{x o c} g(x)$

The limit of a constant times a function is the constant times the limit of the function: $lim_{x o c} [k cdot f(x)] = k cdot lim_{x o c} f(x)$

The limit of a product is the product of the limits: $lim_{x o c} [f(x) cdot g(x)] = lim_{x o c} f(x) cdot lim_{x o c} g(x)$

The limit of a quotient is the quotient of the limits, provided the limit of the denominator is not zero: $lim_{x o c} \frac{f(x)}{g(x)} = \frac{lim_{x o c} f(x)}{lim_{x o c} g(x)}$, if $lim_{x o c} g(x) eq 0$

The limit of a function raised to a power is the limit of the function raised to that power: $lim_{x o c} [f(x)]^n = [lim_{x o c} f(x)]^n$

The limit of a root of a function is the root of the limit of the function: $lim_{x o c} \sqrt[n]{f(x)} = \sqrt[n]{lim_{x o c} f(x)}$

First attempt to evaluate a limit by plugging in the value that x approaches. If it results in a defined value, that is the limit.

Use algebraic manipulation (factoring, rationalizing, etc.) or other techniques to simplify the expression before evaluating the limit.

Limit laws allow you to break down complex limits into simpler parts by dealing with sums, differences, products, quotients, and powers separately.

The Quotient Rule can only be applied if the limit of the denominator is not zero. Otherwise, the limit does not exist or requires further analysis.

If the function is a constant, the limit is simply that constant value, regardless of what x approaches.

One-sided limits examine the behavior of a function as x approaches a value from the left (x -> c-) or from the right (x -> c+).

For a two-sided limit to exist at a point, both the left-hand limit and the right-hand limit must exist and be equal at that point.

Attempt direct substitution. If it yields a defined value, the limit is found. If it yields an indeterminate form, further techniques are required.

Limit laws can be applied when the individual limits of the functions involved exist. They help simplify complex expressions into manageable components.

For a function to be continuous at a point, the limit must exist at that point, the function must be defined at that point, and the limit must equal the function's value at that point.

$lim_{x o c} [f(x) + g(x)] = lim_{x o c} f(x) + lim_{x o c} g(x)$

$lim_{x o c} [f(x) - g(x)] = lim_{x o c} f(x) - lim_{x o c} g(x)$

$lim_{x o c} [k cdot f(x)] = k cdot lim_{x o c} f(x)$

$lim_{x o c} [f(x) cdot g(x)] = lim_{x o c} f(x) cdot lim_{x o c} g(x)$

$lim_{x o c} \frac{f(x)}{g(x)} = \frac{lim_{x o c} f(x)}{lim_{x o c} g(x)}$, if $lim_{x o c} g(x) eq 0$

$lim_{x o c} [f(x)]^n = [lim_{x o c} f(x)]^n$

$lim_{x o c} \sqrt[n]{f(x)} = \sqrt[n]{lim_{x o c} f(x)}$

$lim_{x \to c} k = k$

$lim_{x \to c} x = c$

$lim_{x \to c} x^n = c^n$