Parametric equations, series, and other BC-only concepts tested on AP Calculus BC.
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- If x = f(t) and y = g(t), what is dy/dx in terms of t?
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dy/dx = (dy/dt) / (dx/dt)- What is the formula for the second derivative d²y/dx² for a parametric curve?
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d²y/dx² = (d/dt(dy/dx)) / (dx/dt)- Write the formula for arc length of a parametric curve from t=a to t=b.
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L = ∫[a to b] √((dx/dt)² + (dy/dt)²) dt- What is a vector-valued function?
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A function r(t) = ⟨f(t), g(t), h(t)⟩ that outputs vectors for each input t.- What is the derivative of a vector-valued function r(t) = ⟨f(t), g(t)⟩?
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r'(t) = ⟨f'(t), g'(t)⟩- In polar coordinates, how is the area of a region between two rays and a curve r = f(θ) calculated?
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A = (1/2) ∫[α to β] r² dθ- What is the formula for arc length in polar coordinates from θ=α to θ=β?
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L = ∫[α to β] √(r² + (dr/dθ)²) dθ- What does the Divergence Test (Nth Term Test) for series say?
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If lim(n→∞) aₙ ≠ 0, then the series ∑aₙ diverges. If lim(n→∞) aₙ = 0, the test is inconclusive.- State the Ratio Test for series.
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If lim(n→∞) |aₙ₊₁/aₙ| = L, then the series converges if L < 1, diverges if L > 1, and is inconclusive if L = 1.- State the Root Test for series.
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If lim(n→∞) (|aₙ|)^(1/n) = L, then the series converges if L < 1, diverges if L > 1, and is inconclusive if L = 1.- State the Integral Test for series.
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If f is positive, continuous, decreasing on [1, ∞), then ∑aₙ and ∫[1,∞) f(x) dx both converge or both diverge.- State the Limit Comparison Test for series.
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If lim(n→∞) aₙ/bₙ = c > 0 (finite), then ∑aₙ and ∑bₙ either both converge or both diverge.- What is the Alternating Series Test?
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If aₙ ≥ 0, aₙ₊₁ ≤ aₙ (decreasing), and lim(n→∞) aₙ = 0, then ∑(-1)ⁿaₙ converges.- What is absolute convergence?
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A series ∑aₙ converges absolutely if ∑|aₙ| converges.- What is conditional convergence?
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A series converges conditionally if ∑aₙ converges but ∑|aₙ| diverges.
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