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Duplicate of AP Calculus Theorems Flashcards | StudBud
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Duplicate of AP Calculus Theorems
Duplicate of AP Calculus Theorems
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1
If g(x) = integral of f(t)dt from a to x where a is a constant, then g'(x) = (deriv of x)f(x)
Mean Value Theorem
2nd Form of the Fundamental Theorem of Calculus
Fundamental Theorem of Calculus
Change of Base Property
2
Which theorem is this?
Mean Value Theorem
Fundamental Theorem of Calculus
Rolles Theorem
Extrema Value Theorem
3
Which of the following trig derivatives is wrong?
csc'x = -cscxcotx
cos'x = -sinx
cot'x = -csc2(x)
sec'x = -secxtanx
4
Which theorem is this?
Rolle's Theorem
Fundamental Theorem of Calculus
Mean Value Theorem
Extrema Value Theorem
5
What is the product rule?
d/dx f(g(x)) = f'(g(x)) g'(x)
d/dx (f(x) g(x)) = f(x)g'(x) + g(x) f'(x)
d/dx (g(x)/ h(x)) = (h(x) g'(x) - g(x) h'(x))/ h(x)^2
(d/dx)/(d/dy) = dx?dy
6
Which of the following is not part of the definition of continuity?
lim x→c = 0
lim x→c f(x) exists.
f(c) exists.
lim x→c f(x) = f(c)
7
The picture shows _____?
L'Hospital's Rule
Mean Value Theorem
definition of a derivative
definition of an integral
8
The definition of a derivative is...?
f'(x)=lim h->0 [f(x-h) + f(x)] / h2
f'(c)=lim x->c [f(x) + f(c)] / (x+c)
f'(x)=lim h->0 [f(x+h) - f(x)] / h
f'(c)=lim x->c [f(x) - f(c)] / (x-c)
9
The fundamental theorem of calculus states that The integral on (a, b) of f(x) dx = ____?
F(a) + F(b)
F(b) + F(a)
F(a) - F(b)
F(b) - F(a)
