AP Calculus BC 1.6 Determining Limits Using Algebraic Manipulation - Exam Style Questions - MCQs - New Syllabus

Factor the denominator: \[ a^{2}-x^{2}=(a-x)(a+x)=-(x-a)(a+x). \]
Simplify (for \(x\ne a\)): \[ \frac{x-a}{a^{2}-x^{2}}=-\frac{1}{a+x}. \]
Take the limit: \[ \lim_{x\to a}\left(-\frac{1}{a+x}\right)=-\frac{1}{2a}. \]

✅ Answer: (B)