Calculus Definitions

The process of getting closer to a value.

When different parts of the domain have different functions.

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.

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

When x=a passes through the graph with no interruptions.

• 1. f(a) exists
• 2. limf(x) as x approaches a = f(a)

A line that most resembles a graph at point P.

A line that crosses two points on the graph.

The slope of a tangent

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

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

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

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

The special number that makes its derivitive when x is 0 = one. 

e=2.71828182

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

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.

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

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

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

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

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.

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

When the function changes concavity at x=a.

• 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)

• 1. f''(x)
• 2. y''
• 3. d2y/dx2

• 1. f(g(x))
• 2. fog
• 3. fog(x)