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AP Calculus Flashcards

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11154435208How do you find the zeros of f(x)?Set the function equal to zero. Factor or use the quadratic formula if quadratic. Graph to find the zeros on calculator.0
11154452890How do you know that f(x) is even?Show that f(-x) = f(x). This shows that the graph of f is symmetric to the y-axis.1
11154467062How do you show that f(x) is odd?Show that f(-x) = -f(x). This shows that the graph of f is symmetric to the origin.2
11154485501How do you find the domain of f(x)?Assume domain is (−∞,∞). Restrict domains: denominators ≠ 0, square roots of only non-negative numbers, logarithm or natural log of only positive numbers.3
11154504827How do you find the vertical asymptotes of f(x)?Express f(x) as a fraction, express numerator and denominator in factored form, and do any cancellations. Set denominator equal to 0.4
11154520398How do you find the average rate of change of the function f on [a,b]?5
11154607728How do you find the instantaneous rate of change of the function f at x = a?Find the slope of the tangent line to the function f at x = a. Or, find the derivative of the function at a. Or, find f' (a)6
11154657721How do you factor a sum or difference of cubes?7
11154698752What are the two definitions of the derivative?8
11154817720What is the derivative of sin(u)?9
11154827258What is the derivative of cos(u)?10
11154833485What is the derivative of tan(u)?11
11154849300What is the derivative of csc(u)?12
11154857073What is the derivative of sec(u)?13
11154864224What is the derivative of cot(u)?14
11479178606What is the derivative of ln(u)?15
11479192037ln(a x b)ln(a) + ln(b)16
11479198407ln(a/b) =ln(a)-ln(b)17
11479208692ln(a^b)18
11479222359What is the derivative of e^u?19
11479232271What is the derivative of a^u?20
11687060834How do you find the equation of line normal to a graph at x = c?Find the slope of the tangent line to the graph at x = c, then use the opposite reciprocal slope to write an equation.21
11687103162How do you find horizontal asymptotes of f(x) algebraically?Find the limit if f(x) as x approaches + and - infinity.22
11687119904How do you find vertical asymptotes of f(x) algebraically?Find where the function is undefined. This is usually where the denominator of f(x) = 0.23
11687144040How do you show that f(x) is continuous at x = c?24

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