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

Evaluate x 3+|x-3|/x2-9.

1. 1/6
2. -1/6
3. 1/3
4. 0

Answer

A. 1/6

Solution

For x>3, |x-3|=x-3. Then x-3/(x-3)(x+3)=1/x+3 16. (From the left the limit is - 16.)

More One-Sided Limits and Continuity questions

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

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