Limits, Continuity & Differentiability
Evaluation of Limits
Grade 12
Question:
<p>The value of <span>\(\lim_{x \to \infty} (\sqrt{a^2 x^2 + ax + 1} - \sqrt{a^2 x^2 + 1})\)</span>, where \(a > 0\), is</p>
<p>(a) \(\frac{1}{2}\)</p>
<p>(b) \(-\frac{1}{2}\)</p>
<p>(c) Doesn't exist</p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: Use rationalization to handle the difference of square roots at infinity; divide numerator and denominator by the dominant term.
<p>No solution provided in the page text.</p>
Correct Answer: A