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AP Calculus BC
AP Calculus BC Flash Cards
41
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12th Grade
05/08/2012
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Cards

Term
Local Minimum
 Definition
dy/dx goes (-,0,+) or (-,und,+)
Term
Local Maximum
 Definition
dy/dx goes (+,0,-) or (+,und,-)
Term
d/dx tan(x)
 Definition
sec^2(x)
Term
d/dx cot(x)
 Definition
-csc^2(x)
Term
d/dx sec(x)
 Definition
sec(x)tan(x)
Term
d/dx csc(x)
 Definition
-csc(x)cot(x)
Term
d/dx arcsin(x)
 Definition
1/sqrt(1-x^2)
Term
d/dx arccos(x)
 Definition
-1/sqrt(1-x^2)
Term
d/dx arctan(x)
 Definition
1/(1+x^2)
Term
d/dx arccot(x)
 Definition
-1/(1+x^2)
Term
d/dx arcsec(x)
 Definition
1/(abs(x)sqrt(x^2-1))
Term
d/dx arccsc(x)
 Definition
-1/(abs(x)(x^2-1))
Term
d/dx (a^x)
 Definition
a^x ln(a)
Term
d/dx loga(x)
 Definition
1/(xln(a))
Term
d/dx (uv)
 Definition
udv+vdu
Term
d/dx (u/v)
 Definition
(vdu-udv)/(v^2)
Term
Fundamental Theorem of Calculus
 Definition
Int(f(x),x,a,b)=F(b)-F(a)
where F'(x)=f(x)
Term
d/dx Int(f(t),t,a(x),b(x))=
 Definition
f(b(x))b'(x)-f(a(x))f'(a)
Term
Intermediate Value Theorem
 Definition
f(x) is continuous on [a,b] then any number c between a and b there exists a value d such that f(d)=c
Term
Rolle's Theorem
 Definition
f(x) is continuous [a,b] and f(a)=f(b) and there exists a value c between a and b for some value f(c)=0
Term
Mean Value Theorem
 Definition
f(x) is continuous [a,b] and dy/dx exists then there is a value c such that f'(c)=(f(b)-f(a))/(b-a)
Term
Disk Method
 Definition
V= pi Int(R(x)^2,x,a,b)
Term
Washer Method
 Definition
V = pi Int((R(x)^2-r(x)^2),x,a,b)
Term
ArcLength
 Definition
L = Int(sqrt(1+(f'(x))^2),x,a,b)
Term
Velocity
 Definition
D/dt(position)
Term
Acceleration
 Definition
d/dt(Velocity)
Term
Velocity Vector
 Definition
Term
Speed = abs(V)
 Definition
sqrt((x')^2+(y')^2)
Term
Distance
 Definition
Int(abs(V),t,initial,final)
Term
Average Velocity
 Definition
(Final Position-Initial Position)/Time
Term
Int(u,v)
 Definition
uv-Int(v,u)
Term
Int(ln(x),x)
 Definition
xln(x)-x+C
Term
Taylor Series
 Definition
(f(0)x^0)/0!+(f'(0)x^1)/1!+(f''(0)x^2)/2!
Term
Maclaurin for e^x
 Definition
1+x+x^2/2+x^3/3...
Term
Maclaurin for cos(x)
 Definition
1-x^2/2+x^4/4...
Term
Maclaurin for sin(x)
 Definition
x-x^3/3!+x^5/5!
Term
Maclaurin for 1/(1-x)
 Definition
1+x+x^2+x^3...
Term
Taylor Series for ln(x+1)
 Definition
x-x^2/2+x^3/3-x^4/4
Term
Ratio Test
 Definition
Sigma(a sub k, k=0, infinity) converges if
lim k->inf abs((a sub k+1)/(a sub k))<1
Term
Area of a Polar
 Definition
1/2 Int(r(theta)^2,theta,a,b)
Term
Derivative of a Polar
 Definition
dy/dx = (dy/dtheta)/(dx/dtheta)
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