# Shared Flashcard Set

## Details

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

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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