Calculus 1 Common Topics List1 1. Functions (a) polynomials, rationals, exponentials, logarithmic, trigonometric, arctan, absolute value, radicals, power function i. graphs ii. continuity properties (b) inverse functions (c) composition of functions (d) functional notation (e) functions of two variables, i.e. f(x,y) 2. Limits (a) intuitive denition i. graph ii. table (b) right- and left-hand limits (c) analytical procedures for computing limits (d) limit laws (properties of limits) (e) indeterminate forms (∞ and 0) ∞ 0 (f) successive approximations (judging accuracy subjectively through iterations, i.e. two approximations of the same result are better than one) 3. Continuity (a) ...
AP CALCULUS FORMULA LIST 1n Definition of e: e = lim1+ n→∞ n ____________________________________________________________________________________ x if x≥0 Absolute Value: x = −x if x < 0 ____________________________________________________________________________________ Definition of the Derivative: f (x+x)− f (x) f (x+h)− f (x) f '(x) = lim f '(x) = lim x→∞ x h→∞ h f (a +h)− f (a) f '(a) = lim derivative at x = a h→∞ h f (x)− f (a) f '(x) = lim alternate form x→a x−a ____________________________________________________________________________________ Definition of Continuity: f ...
2020 AP CALCULUS AB FORMULA LIST ______________________________________________________________________________ Definition of the derivative: f xh f x f x f a (Alternative form) fx( ) lim falim h0 h xa xa ____________________________________________________________________________ Definition of continuity: f is continuous at c if and only if 1) f (c) is defined; 2) lim fx( ) exists; xc 3) lim f (x) f (c). xc ____________________________________________________________________________________________________ Mean Value Theorem: If f is continuous on [a, b] and differentiable on (a, b), then there f b f a exists a number c on (a, b) such that fc( ) ba . _____________________________________________________________________________________________________ Intermediate Value Theorem: If f ...
2020 AP CALCULUS BC FORMULA LIST ______________________________________________________________________________ Definition of the derivative: f xh f x f x f a (Alternative form) fx( ) lim falim h0 h xa xa ____________________________________________________________________________ Definition of continuity: f is continuous at c if and only if 1) f (c) is defined; 2) lim fx( ) exists; xc 3) lim f (x) f (c). xc ____________________________________________________________________________________________________ Mean Value Theorem: If f is continuous on [a, b] and differentiable on (a, b), then there f b f a exists a number c on (a, b) such that fc( ) ba . _____________________________________________________________________________________________________ Intermediate Value Theorem: If f ...
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