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Calculus Memorization
Definitions and theorems that must be memorized
8
Mathematics
12th Grade
11/09/2010

Additional Mathematics Flashcards

 


 

Cards

Term
Conditions for continuity at a point
Definition

Function exists

Limit exists

Limit is equal to function

Term
Conditions where a function is not differentiable
Definition

Corners / Cusps

Vertical tangents

Discontinuities

Term
Definition of a corner or cusp
Definition
Slope from left does not equal slope from right
Term
Product rule
Definition

(First)*(derivative of second)+(second)*(derivative of first)

 

or

 

uv'+vu'

Term
quotient rule
Definition
(bottom)(derivative of top) - (top)(derivative of bottom) all over (bottom)2
Term
Intermediate value theorem -- functions
Definition

if f(x) is continuous on (a,b)

 

Then f(x) will pass through every value between f(a) and f(b) at least once on the interval (a,b)

Term
Intermediate value theorem -- derivatives
Definition

if f(x) is differentiable on (a,b)

 

then f'(x) takes every value between f'(a) and f(b) at least once on the interval (a,b)

Term
If it's differentiable...
Definition
Then it's continuous
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