Study AP Calculus AB with flashcards covering limits, derivatives, integrals, and the fundamental theorems you need to know for the exam.
Must-Know AP Calculus AB Formulas and Theorems
- Fundamental Theorem of Calculus (Part 1): If F(x) = ∫[a to x] f(t) dt, then F'(x) = f(x). The derivative of an integral with a variable upper bound is the integrand evaluated at that bound.
- Fundamental Theorem of Calculus (Part 2): ∫[a to b] f(x) dx = F(b) − F(a), where F is any antiderivative of f. Connects differentiation and integration.
- Chain Rule: d/dx [f(g(x))] = f'(g(x)) · g'(x). Apply when differentiating a composite function — differentiate outer function (leaving inner alone), multiply by derivative of inner.
- Mean Value Theorem: If f is continuous on [a, b] and differentiable on (a, b), then there exists c in (a, b) such that f'(c) = [f(b) − f(a)] / (b − a).
- L'Hôpital's Rule: If lim f(x)/g(x) gives 0/0 or ∞/∞, then lim f(x)/g(x) = lim f'(x)/g'(x). Only apply to indeterminate forms.
- Integration by Parts: ∫u dv = uv − ∫v du. Choose u to be the function that simplifies when differentiated (LIATE order: Logarithmic, Inverse trig, Algebraic, Trig, Exponential).
- Squeeze Theorem: If g(x) ≤ f(x) ≤ h(x) near a and lim g(x) = lim h(x) = L, then lim f(x) = L.
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