AP Calculus AB Review Pt. 1 Flashcards
Formulas and Concepts from AP Calculus AB.
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| 755456713 | The existence or nonexistence of f(x) at x=c has no bearing on the existence of what? | The limit of f(x) as x approaches e | 1 | |
| 755456714 | What are the three common types of behavior associated with the nonexistence of a limit? | 1. f(x) approaches a different number from the right side of c than it approaches from the left side of c 2. f(x) increases or decreases without bound as x approaches c (asymptote). 3. f(x) oscillates between two fixed vales as x approaches e | 2 | |
| 755456715 | What is lim (x→c) b? | b | 3 | |
| 755456716 | What is lim (x→c) x? | c | 4 | |
| 755456717 | What is lim (x→0) x''? | c'' | 5 | |
| 755456718 | What is lim (x→0) √x | Does not exist | 6 | |
| 755456719 | 0/0 is called what? | Indeterminate form | 7 | |
| 755456720 | lim (x→0) [sinx / x] = | 1 | 8 | |
| 755456721 | lim (x→0) [(1-cosx) / x] = | 0 | 9 | |
| 755456722 | lim (x→0) [x / (sinx)] = | 0 | 10 | |
| 755456723 | In common sense terms, a function is continuous at x=c if you don't have what three things at c? | 1. no holes 2. no jumps/gaps 3. no asymptotes | 11 | |
| 755456724 | By the definition of continuity, a function is continuous at x=c if what three conditions are met? | 1. f(c) is defined 2. lim (x→c) f(x) exists 3. lim (x→c) f(x) = f(c) | 12 | |
| 755456725 | By the definition of a limit, when does lim (x→c) f(x) = L | 1. limit from the right equal the limit from the left 2. lim (x→c⁺) f(x) = lim (x→c⁻) f(x) = L | 13 | |
| 755456726 | Continuity can be destroyed by any one of what three conditions? | 1. the function is not defined at x=c 2. the limit of f(x) does not exist at x=c 3. the limit of f(x) exists at x=c, but is not equal to f(c) | 14 | |
| 755456727 | When is a function continuous on the open interval (a,b)? | When f is continuous at each point in the interval (a,b) | 15 | |
| 755456728 | When is f continuous everywhere? | When f is continuous on the entire real line (-∞,∞) | 16 | |
| 755456729 | What are the two types of discontinuity? | Removable and nonremovable | 17 | |
| 755456730 | What is another term for non-removable discontinuity? | Essential | 18 | |
| 755456731 | If a discontinuity at x=c can be made continuous by appropriately defining or redefining f(c), then f has what type of discontinuity | Removable | 19 | |
| 755456732 | Is lim (x→c⁺) f(x) a limit from the right or left? | Right | 20 | |
| 755456733 | Is lim (x→c⁻) f(x) a limit from the right or left? | Left | 21 | |
| 755456734 | lim (x→0⁺) ⁿ√x = | 0 | 22 | |
| 755456735 | If n is even, lim (x→0⁻) ⁿ√x = | DNE | 23 | |
| 755456736 | What is [x]? | Greatest integer function | 24 | |
| 755456737 | If f and g are continuous at x=c, then what else is continuous at x=c? | 1. scalar multiple: bf and bg 2. sum: f+g 3. difference: f-g 4. product fg 5. Quotient: f/g if g(c)≠0 | 25 | |
| 755456738 | What is the Intermediate Value Theorem | If f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b), then there is at least one number c in [a,b] such that f(c)=k | 26 | |
| 755456739 | What is an infinite limit? | A limit in which f(x) increases or decreases with bound | 27 | |
| 755456740 | If f decreases without bound, what does the limit approach? | ∞ | 28 | |
| 755456741 | If f decreases without bound, what does the limit approach? | ⁻∞ | 29 | |
| 755456742 | To prove that x=c is a vertical asymptote, what two choices do you have to justify your answer? | 1. lim (x→c⁺) f(x) = ∞ or ⁻∞ 2. lim (x→c⁻) f(x) = ∞ or ⁻∞ | 30 |