Engineering Board Exam Reviewer · One-Sided Limits and Continuity · easy

Let f(x)= casesx+1, & x<3\ 9-x, & x≥3 cases. Find x 3+f(x).

1. 4
2. 5
3. 6
4. 9

Answer

C. 6

Solution

For x>3 the rule is 9-x, so the right-hand limit is 9-3=6. (The left-hand limit is 3+1=4, so f is not continuous at 3.)

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2. Evaluate: x 0-1/x
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5. Determine whether x 2|x-2|/x-2 exists.
6. Determine the type of discontinuity, if any, of f(x)=1/x-3 at x=3.
7. Evaluate x 3+|x-3|/x2-9.
8. Find the value of k that makes f(x)= casesx2+k, & x<3\ 2x+1, & x≥3 cases continuous at x=3.

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