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Formulas for AP Calc BC
Review for AP Exam
11
Mathematics
Undergraduate 1
05/01/2011
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Term
Area under a Polar Curve
 Definition
A=½∫r²dθ
Term
Taylor Series
 Definition

f(x)=∑((f(K)(c)/K!)(x-c)K

)
Term
Taylor Lagrange Error Bound
 Definition

Rn(x)≤|(f(n+1)(c))/(n+1)!)(x-a)n+1

|
Term
Arc Length
 Definition
S=∫√(1+[f'(x)2])dx
Term
Exponential Growth
 Definition
dy/dt=ky and y=y0ekt
Term
Logistic Growth
 Definition
dP/dt=kP(M-P) and P=M/(1+Ae-Mkt)
Term
d/dx[sin-1u]
 Definition

du/dx

√(1-u²)
Term
d/dx[tan-1u]
 Definition

du/dx

1+u2
Term
d/dx[sec-1u]
 Definition

du/dx

|u|√(u2-1)
Term
cos(2θ)
 Definition

=2cos2θ-1

=1-2sin2θ

=cos2θ-sin2θ
Term
Trig Identities
 Definition

sin2θ+cos2θ=1

tan2θ+1=sec2θ

cot2θ+1=csc2θ
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