Engineering Board Exam Reviewer · Limits · medium

Evaluate: x 0 sqrt(x+9)-3x

1. 1/6
2. 1/3
3. 0
4. 1/9

Answer

A. 1/6

Solution

Multiplying by the conjugate: sqrt(x+9)-3x· sqrt(x+9)+3sqrt(x+9)+3= xx(sqrt(x+9)+3)= 1sqrt(x+9)+3, which approaches 1/6 as x 0.

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