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Math
Calculus
BC Calc Test III
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Terms in this set (8)
if f is continuous on an open interval containing a, then for every x in the interval: d/dx [a∫b f(x)dx] = f(x)
if the first function is g(x) then g'(x) = f(x)
the derivative of an integral function like g(x) is the upper limit plugged in
FTC I
if F is the antiderivative of f on a closed interval [a,b] then:
a∫b f(x)dx = F(b) -F(a); a∫b f'(x)dx = f(b) - f(a)
this is how you find area without drawing the graph
FTC II
(x(b) - x(a))/b-a
same for acceleration but with velocity
velocity
sum of absolute values of displacements between changes in direction -- you find changes in direction through inflection points
a∫b |v(t)|
total distance formula
If the limit as x approaches c f(x)/g(x) = 0/0 or the limit as x approaches c f(x)/g(x) = ∞/∞, then the limit as x approaches c of f(x)/g(x) = the limit as x approaches c of f'(x)/g'(x)
L'Hopitals Rule
(f(b)-f(a))/b-a
average rate of change in y
If f is continuous on [a,b[, then there is a c in [a,b] such that
f(c)(b-a) = a∫b f(x)dx
and f(c) = (1/(b-a))a∫b f(x)dx is the average value of f on [a,b]
MVT for Integrals
1/2 (h) (b + 2b₂ + 2b₃ + ... 2bₙ_₁ + bₙ)
Trapezoid Area Sums with equal intervals
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