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education/math/MATH1210 (calc 1)/Limits.md
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@ -26,6 +26,26 @@ Formally, a function $f$ is continuous at a point $a$ if:
- $\lim_{x \to a} f(x)$ exists - $\lim_{x \to a} f(x)$ exists
- $\lim_{x \to a} = f(a)$ - $\lim_{x \to a} = f(a)$
- A function is continuous on the open interval $(a, b)$ if it is continuous at all points between $a$ and $b$
- A function is continuous on the closed interval $[a, b]$ if it is continuous at all points between $a$ and $b$
# Elementary Functions
An elementary function is any function that is defined using:
- Polynomial functions
- Rational functions
- Root functions
- Trig functions
- Inverse trig functions
- Exponential functions
- Logarithmic functions
- Operations of:
- Addition
- Subtraction
- Multiplication
- Division
- Composition
A piece-wise function is *not* considered an elementary function
# Definitions # Definitions
| Term | Definition | | Term | Definition |