# Calculus Definitions

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The flashcards below were created by user hsu.kaitlyn on FreezingBlue Flashcards.

1. Limit
The process of getting closer to a value.
2. Split Function
When different parts of the domain have different functions.
3. 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.
4. Limit at infinity
As x approaches infinity f(x) approaches a value=HA or infinity=DNE
5. 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)
6. Tangent
A line that most resembles a graph at point P.
7. Secant
A line that crosses two points on the graph.
8. The Derivitive Function
The slope of a tangent
9. 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
10. Implicit Differentiation
Differentiating both sides with respect to x when y is embedded in the equation.
11. Composition
The process of combining two functions to create a new one.
12. Decomposition
The process of identifying two functions such that they create the given function through composition.
13. Euler's Number
The special number that makes its derivitive when x is 0 = one.

e=2.71828182
14. Natural logarithm
The logarithm with base e. Written ln(x). Its function is also the inverse of y=e^x
15. 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.
16. Absolute Min
if f(c) _< f(x) fo any x value in the domain of f(x), then f(c) is called absolute minimum.
17. 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
18. Fermat's Thereum
if f(x) has a local max or min at c, then either f'(x)=0 or f'(x)=undefined.
19. Local max/min
When f(c)_> or _< f(x) in the neighbourhood of a value.
20. 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.
21. 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.
22. Point of Inflection
When the function changes concavity at x=a.
23. 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)
24. Notation for second derivitive
• 1. f''(x)
• 2. y''
• 3. d2y/dx2
25. Notation for Composite Functions
• 1. f(g(x))
• 2. fog
• 3. fog(x)

## Card Set Information

 Author: hsu.kaitlyn ID: 254163 Filename: Calculus Definitions Updated: 2013-12-23 17:47:47 Tags: Limits Derivitives Optimization Curve sketching Folders: Description: All about Calculus :) Show Answers:

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