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Questions and Answers
Which of the following is the correct definition of a limit of a function?
Which of the following is the correct definition of a limit of a function?
- The value of the function at a specific number
- The value that the function approaches as x approaches negative infinity
- The value that the function approaches as x approaches a specific number (correct)
- The value that the function approaches as x approaches infinity
In evaluating the limit of a function, we are concerned with the values of x in an open interval containing a but not a itself. Why is this important?
In evaluating the limit of a function, we are concerned with the values of x in an open interval containing a but not a itself. Why is this important?
- The limit is only defined for values of x less than a
- The limit is only defined for values of x greater than a
- The limit is always equal to the value of the function at a
- The limit is undefined if a is included in the interval (correct)
Which of the following is a possible case when evaluating the limit of a function?
Which of the following is a possible case when evaluating the limit of a function?
- f(a) exists and f(a) = L
- f(a) is undefined
- f(a) exists, but f(a) ≠L
- All of the above (correct)
What is the limit of the function $f(x) = x + 3$ as x approaches 3?
What is the limit of the function $f(x) = x + 3$ as x approaches 3?
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What is the limit of the function $g(x) = \frac{x^2-9}{x-3}$ as x approaches 3?
What is the limit of the function $g(x) = \frac{x^2-9}{x-3}$ as x approaches 3?
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