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8 Cards in this Set

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FTC
if a function is continuous on [a,b] and F is the antiderivative of f on the interval [a,b] then

[∫b to a] f(x) d(x)= f(b) - f(a)
MVT
if f is continous on the closed then there exists a number c between [a,b] such that:

f'(c)= f(b) - f(a) / b - a
average rate of change
slope
average value of a function
f(c)= 1/(b-a) [∫b to a] f(x) dx
rolle's theorm
if f is continuos on [a,b[ and differentiable on (a,b) and f(a)=f(b)
then there exists a c such that f'(c)=0
EVT
if f is cont. on [a,b] then there must exist a min and a max
IVT
if f is cont. on [a,b] and the number k exists btwn f(a) and f(b), then there much be one number c in [a,b] such that f(c)=k
for a limit to EXIST..
the limit from the left must be equivalent to the limit on the right