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

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.

1. 2
2. 1
3. 0
4. undefined

Answer

A. 2

Solution

For x 1, f(x)=(x-1)(x+1)/x-1=x+1, so x 1f(x)=2. For continuity, k must equal this limit: k=2.

More One-Sided Limits and Continuity questions

1. For what value of k is f(x)= casesx+k, & x<2 2, & x≥2 cases continuous at x=2?
2. Determine whether x 2|x-2|/x-2 exists.
3. Determine the type of discontinuity, if any, of f(x)=1/x-3 at x=3.
4. Evaluate: x 0+1/x
5. Evaluate: x 0-1/x

All One-Sided Limits and Continuity questions