Unit 1 - Limits Flashcards
AP Calculus AB
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| 457377055 | Limits | how the output of a function behaves as the input APPROACHES some value | |
| 457377056 | Right-hand limit | the limit of f as x approaches c from the right | |
| 457377057 | Left-hand limit | the limit of f is x approaches c from the left | |
| 457377058 | Continuous function (on an interval) | a function whose output vary continuously with the inputs & do not jump from one value to another without taking on the values in between on the given interval | |
| 457377059 | continuous function | a function that is continuous at every point on ITS DOMAIN | |
| 457377060 | continuity at a point | f(x) is continuous at an INTERIOR POINT c of its domain if lim x->c f(x) = f(c) ---> a. f(c) is defined (exists) b.lim x->c f(x) exists c. lim x->c f(x) = f(c) | |
| 457377061 | Types of discontinuities | Removable (hole), infinite, jump, oscillating | |
| 457377062 | Composite functions | if f is continuous at c & g is continuous at f(c), then the compost f o g is continuous at c | |
| 457377063 | Intermediate Value Theorem (IVT) | a function y = f(x) that is continuous on a closed interval [a,b] takes on every value between f(a) and f(b) | |
| 457377064 | Infinite Limits | when f approaches infinity as x approaches a, the limit does not exist, & is called UNBOUNDED | |
| 457377065 | Vertical Asymptote | the line x=a is a vertical asymptote if & only if 1. limit x->a+ f(x) = + - infinity 2. limit x->a- f(x) = + - infinity |