AP Calculus BC

All of AB plus parametrics, polar, vectors, and infinite series.

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What's in Calc BC

Every unit is mapped to the official Course and Exam Description.

U1AB Topics

U2Parametric, Polar, Vector

U3Infinite Sequences & Series

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6 matches

Q1Serieshard

Which test would you use first to determine convergence of the series Σ(1/n²) for n=1 to ∞?

Q2Integrationhard

What is ∫ 1/(x² + 4) dx?

Q3Parametrichard

If x = t² and y = t³, what is dy/dx at t = 2?

Q4Serieshard

The Maclaurin series for eˣ is Σ(xⁿ/n!) from n=0 to ∞. What is the Maclaurin series for e^(2x)?

Sample FRQ · AI graded

FRQ prompt

Free Response Question:
(a) Find the interval of convergence for the power series Σ (3x)ⁿ / n from n=1 to ∞. Show all work including the Ratio Test and endpoint checks.

(b) Write the Taylor series for ln(1+x) centered at x = 0, up to and including the x⁴ term.

(c) Use your series from part (b) to approximate ln(1.1) to four decimal places.

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