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4 Cards in this Set
- Front
- Back
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Does a function need to be defined for a given input to have a limit at that input?
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No
Explanation: A function only needs to be arbitrarily close to a certain value, approaching from both directions to have a limit at that value. |
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True/False: If a function is continuous for a certain x-value, then the function has a limit at that value.
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True
Explanation: If it is continuous at a value it is defined there and in an arbitrarily close area, so the limit will also exist. |
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True/False:
A function can have a limit when the right hand and left hand limits are different. |
False
Explanation: If the right hand and left hand limits are different the function is approaching two different locations from the two directions and fails to meet the definition of a limit. |
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True/False:
If a function is continuous at a point it is also differentiable at that point. |
False
Explanation: A "corner" for the graph would be a counterexample for the statement. |
