Study AP Calculus BC with flashcards covering all AB content plus the BC-only topics: series, polar coordinates, parametric equations, and advanced integration techniques.
BC-Only Topics: Series and Convergence
- Taylor Series: f(x) = Σ f^(n)(a)/n! · (x−a)^n. Represents a function as an infinite polynomial centered at x = a. Maclaurin series is a Taylor series centered at a = 0.
- Ratio Test: For Σ aₙ, compute L = lim |aₙ₊₁/aₙ|. If L < 1: converges absolutely. If L > 1: diverges. If L = 1: inconclusive.
- Alternating Series Test: Σ (−1)^n bₙ converges if (1) bₙ is decreasing and (2) lim bₙ = 0. Error bound: |error| ≤ first omitted term.
- Radius of Convergence: The value R such that a power series Σ cₙ(x−a)^n converges for |x−a| < R and diverges for |x−a| > R. Found using ratio or root test.
- Arc Length (Parametric): L = ∫ √[(dx/dt)² + (dy/dt)²] dt. For a Cartesian curve: L = ∫ √[1 + (dy/dx)²] dx.
- Euler's Method: Numerical approximation of ODEs: yₙ₊₁ = yₙ + h·f(xₙ, yₙ). Step size h affects accuracy — smaller steps give better approximations.
- Logistic Growth: dP/dt = kP(1 − P/L). Population grows rapidly when small, slows near carrying capacity L. Solution: S-shaped curve.
AP Calculus BC Practice Questions · AP Calc BC Study Guide · How to Get a 5 on AP Calc BC
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