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Limits & Continuity
| Question | Answer |
|---|---|
| What is the limit definition of a continuous function? | f(x) is continuous iff the function is defined at x = a, the limit of f(x) as x -> a exists, and the limit of f(x) as x -> a = f(a). |
| What is a discontinuous function? | A function with a jump, hole, or asymptote. |
| What is a step discontinuity (jump)? | A discontinuity for which the graph steps or jumps from one connected piece of the graph to another. |
| What is a removable discontinuity (hole)? | A removable discontinuity is a point on the graph that is missing or separate from the rest of the function. |
| What is an infinite discontinuity? | A graph which approaches one or more asymptotes, resulting in a graph that cannot be drawn without lifting up your pencil. |
| What is the definition of a limit? | A prediction of a function's y value based on it's behavior at x-values very close to the point you're interested in. |
| What is the Intermediate Value Theorem? | If f is continuous on [a,b] and there is a value of k between f(a) and f(b), then there exists at least one value of c on (a,b) such that f(c)=k |
| limx→0 sin(x)/x = | 1 |
| limx→∞ sin(x)/x = | 0 |
| limx→0 cos(x-1)/x = | 0 |
Created by:
amvach
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