Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
| Lim as x approaches a exists |
|
Definition
| If the right hand derivative and the left hand derivative are equal |
|
|
Term
| f(x) is continuous at x=a if |
|
Definition
| limit as x approaches a of f(x) equals f(x) |
|
|
Term
| f'(x) at x = a and its four equivalent interpretations |
|
Definition
lim as h approaches 0 of f(a+h)-f(a)/h exists.
1. derivative at x=a
2. velocity at x=a
3. instant rate of change
4. slope |
|
|
Term
| Mean Value Theorem- differentiable |
|
Definition
| if f(x) is continuous over [a,b], differentiable over (a,b), then there exists some c in [a,b] such that f'(c)=f(b)-f(a)/b-a |
|
|
Term
| Mean Value Theorem- integrable |
|
Definition
| if f(x) is an integrable function over [a,b], then there exists some C(y-value) such that the integral from a to b = c(b-a) |
|
|
Term
| Fundamental Theorem of Calculus 1 and 2 |
|
Definition
FTC 1: if f(x) is continuous then the integral from 0 to x equals f(x)
FTC 2: if F(x) is any anti-derivative of f(x)then the integral of f(x) from a to b is F(b)- F(a) |
|
|
