1/31/2024 0 Comments Bc calculus cheat sheet![]() ![]() Series must converge to a value that is >X** **Note: if the integral converges to X, then the Integral test If f(x) is positive, continuous, and If a smaller function diverges: larger function If a larger function converges: smaller function ![]() If ∑ |□ converges, is absolutely convergentĭirect Comparison Test (DCT) Provided that both are positive: If |□| ≥ 1, the geometric series diverges ![]() Varying height (given by a function like ℎ(□)) s × ℎ(□)where s is the Isosceles right triangle w/ hypotenuse in base region 1 Where the slope is increasing at its maximum □/2 is a point of inflection (the graph changesįrom concave up to concave down). This document is not inclusive of all formulas, and definitely not of all topics.The parts highlighted in green are topics covered in AP Calc AB but not AP Calc BC.Differentiation Rules Chain Rule ( ) '( ) d du f u f u dx dx = Product Rule ( ) d dv du uv u v dx dx dx = + Quotient Rule 2 du dv v u d u dx dx dx v v − = Properties of Log and Ln ( ) ( ) 1 1 0 2 3 4 5 6 a ln x n a b. 2 2 d y dx goes (+,0,-),(-,0,+), (+,und,-), or (-,und,+) Mean Value & Rolle’s Theorem If the function f(x) is continuous on and the first derivative exists on the interval (a, b), then there exists a number x = c on (a, b) such that ( ) ( ) '( ) f b f a f c b a − = − if f(a) = f(b), then f ’(c) = 0. ![]() local minimum: dy dx goes (-,0,+) or (-,und,+) or 2 2 0 d y dx > local maximum: dy dx goes (+,0,-) or (+,und,-) or 2 2 0 d y dx < Absolute Max/Min.: Compare local extreme values to values at endpoints. Download ap calculus bc cheat sheet and more Cheat Sheet Calculus in PDF only on Docsity! AP CALCULUS BC Stuff you MUST Know Cold l’Hopital’s Rule ( ) 0 If or = ( ) 0 f a g a ∞ = ∞, then ( ) '( ) lim lim ( ) '( )x a x a f x f x g x g x→ → = Definition of Derivative (slope of the tangent line) 0 ( ) ( ) '( ) lim h f x h f x f x h→ + − = Average Rate of Change (slope of the secant line) If the points (a, f(a)) and (b, f(b)) are on the graph of f(x) the average rate of change of f(x) on the interval is ( ) ( )f b f a b a − − Derivatives ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 2 sin cos cos sin tan sec cot csc sec tan sec csc cot csc 1 1 n n u u a u x d x nx dx d x x dx d x x dx d x x dx d x x dx d x x x dx d x x x dx d lnu du dx u d e e du dx d log x dx x ln a d a a ln a du dx −= − = − = − = Curve sketching and analysis y = f(x) must be continuous at each: critical point: 0 dy dx = or undefined. ![]()
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