AP Calculus BC - Stuff You Must Know

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This includes a ton of stuff you must remember for the AP Test. It includes equations, theories, rules, derivatives, integrals, and more. I only recommend using these as flashcards or multiple choice only.

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60 Terms

1
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L'Hôpital's Rule
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Slope of a Parametric equation
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Euler’s Method
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Polar Area
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Polar Slope
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Integration by parts
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Integral of logarithms
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Ratio Test
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sin(2x)
2sin(x)cos(x)
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cos(2x)
cos^2(x) - sin^2(x)
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cos(2x)
1 - 2sin^2(x)
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cos^2(x)
1/2(1+cos(2x))
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sin^2(x)
1/2(1-cos(2x))
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sin^2(x) + cos^2(x)
1
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1+tan^2(x)
sec^2(x)
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cot^2(x) + 1
csc^2(x)
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sin(-x)
\-sin(x)
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cos(-x)
cos(x)
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Taylor Series
f(x) = f(a) + f’(a)(x-a) + \[f’’(a)(x-a)^2 / 2!\] + \[f’’’(a)(x-a)^3 / 3!\] + …
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Lagrange Error Bound
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Maclaurin Series
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Alternating Series Error Bound
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Geometric Series
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sin(0)
0
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cos(0)
1
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tan(0)
0
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sin(pi/6)
1/2
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cos(pi/6)
root3/2
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sin(pi/4)
root2/2
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cos(pi/4)
root2/2
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sin(pi/3)
root3/2
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cos(pi/3)
1/2
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sin(pi/2)
1
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cos(pi/2)
0
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Chain Rule
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Product Rule
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Quotient Rule
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Trapezoidal Rule
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NEVER FORGET (for integrals)
\+C
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Average Value
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d/dx sin(x)
cos(x)
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d/dx cos(x)
\-sin(x)
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d/dx tan(x)
sec^2(x)
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d/dx cot(x)
\-csc^2(x)
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d/dx sec(x)
sec(x)tan(x)
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d/dx csc(x)
\-csc(x)cot(x)
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d/dx ln(u)
1/u
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term image
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Solid Disk Method
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Solid Washer Method
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Cartesian Arc Length
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Polar Arc Length
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Parametric Arc Length
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Intermediate Value Theorem
If the function f(x) is continuous on \[a,b\], then f(x) achieves every value between f(a) and f(b) in the open interval (a,b).
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Mean Value Theorem
If the function f(x) continuous on \[a,b\], and the first derivative exists on the interval (a,b), then there is at least one number x = c in (a,b) such that f’(c) = \[ f(b)-f(a) \] / (b-a).
If the function f(x) $$continuous on \[a,b\], and the first derivative exists on the interval (a,b)$$, then there is at least one number x = c in (a,b) such that f’(c) = \[ f(b)-f(a) \] / (b-a).
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Rolle’s Theorem
Same as mean value theorem but if f(a) = f(b), then there is at least one number x = c in (a,b) such that f’(c) = 0.
Same as mean value theorem but if f(a) = f(b), then there is at least one number x = c in (a,b) such that f’(c) = 0.
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d/dx loga(x)
1/xln(a)
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Displacement
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Speed
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Distance
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