# Calculus Definitions

 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) exists2. 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) exists2. f(x) is continuous at x=a f(x) is not differentiable at...1. Discontinuities2. Vertical tangent2. 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/dx2.y'3. y'= slope of tangent/@ (a, f(a)) to y=f(x)4. f'(x) = roc @ x= a5. df(x)/x6. Dxf(x) Notation for second derivitive 1. f''(x)2. y''3. d2y/dx2 Notation for Composite Functions 1. f(g(x))2. fog3. fog(x) Authorhsu.kaitlyn ID254163 Card SetCalculus Definitions DescriptionAll about Calculus :) Updated2013-12-23T17:47:47Z Show Answers