Limit of a function

\underset{x \to x_{0}}{l i m} c = c, c \in ℝ

\underset{x \to x_{0}}{l i m} [c \cdot f (x)] = c \cdot \underset{x \to x_{0}}{l i m} f (x) c \in ℝ

If both functions have finite limits, then

\underset{x \to x_{0}}{l i m} [f (x) \pm g (x)] = \underset{x \to x_{0}}{l i m} f (x) \pm \underset{x \to x_{0}}{l i m} g (x)

\underset{x \to x_{0}}{l i m} [f (x) \cdot g (x)] = \underset{x \to x_{0}}{l i m} f (x) \cdot \underset{x \to x_{0}}{l i m} g (x)

\underset{x \to x_{0}}{l i m} [\frac{f (x)}{g (x)}] = \frac{\underset{x \to x_{0}}{l i m} f (x)}{\underset{x \to x_{0}}{l i m} g (x)}, \underset{x \to x_{0}}{l i m} g (x) \neq 0

Keywords: limit of a function, properties

Important functions
Linear polynomial function
Quatratic polynomial function
Cubic polynomial function
Rational function
Root function with even radical
Root function with odd radical
Exponential function
Logarithmic function
Sine function
Cosine function
Tangent function
Cotangent function
Absolute value functions
Function Transformations
Variable and function value transformations
Limits
Limit of a function
Dervation
Table of Derivatives
Differentiation rules
Taylor Series
Integration
Table of Integrals
Integration Rules
Definite Integrals