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Limit
The process of getting closer to a value.

Split Function
When different parts of the domain have different functions.

Infinite Limit
When f(x) approaches infinity was x gets closer to a value. When the limit as x approaches a = infinity there is a VA at x=a and the limit does not exist.

Limit at infinity
As x approaches infinity f(x) approaches a value=HA or infinity=DNE

Continuous Function
When x=a passes through the graph with no interruptions.
 1. f(a) exists
 2. limf(x) as x approaches a = f(a)

Tangent
A line that most resembles a graph at point P.

Secant
A line that crosses two points on the graph.

The Derivitive Function
The slope of a tangent

Differentiability
The ability to find the derivitive.
 f(x) is differentiable if..
 1. f'(a) exists
 2. f(x) is continuous at x=a
 f(x) is not differentiable at...
 1. Discontinuities
 2. Vertical tangent
 2. Sudden change in slope

Implicit Differentiation
Differentiating both sides with respect to x when y is embedded in the equation.

Composition
The process of combining two functions to create a new one.

Decomposition
The process of identifying two functions such that they create the given function through composition.

Euler's Number
The special number that makes its derivitive when x is 0 = one.
e=2.71828182

Natural logarithm
The logarithm with base e. Written ln(x). Its function is also the inverse of y=e^x

Logarithmic Differentiation
When there is a function that is like x^x that is non polynomial, non exponential, apply ln to each side and move the exponent to the front then do Implicit Differentiation.

Absolute Min
if f(c) _< f(x) fo any x value in the domain of f(x), then f(c) is called absolute minimum.

Absolute Max
if f(c) _> f(x) for any x value in the domain of f(x), than f(c) is called absolute maximum. It is usually within a closed interval

Fermat's Thereum
if f(x) has a local max or min at c, then either f'(x)=0 or f'(x)=undefined.

Local max/min
When f(c)_> or _< f(x) in the neighbourhood of a value.

Concave up
The graph of y=f(x) is called Concave Up on the interval (a,b) if the graph lies above its tangents on the interval.

Concave Down
The graph y=f(x) is called Concave Down on the interval (a,b) if the graph lies below its tangents on the interval.

Point of Inflection
When the function changes concavity at x=a.

Notation for Derivitive
 1. dy/dx
 2.y'
 3. y'= slope of tangent/@ (a, f(a)) to y=f(x)
 4. f'(x) = roc @ x= a
 5. df(x)/x
 6. Dxf(x)

Notation for second derivitive
 1. f''(x)
 2. y''
 3. d2y/dx2

Notation for Composite Functions
 1. f(g(x))
 2. fog
 3. fog(x)

