Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>Find the largest non-negative integer a for which limx→1
n
−ax+sin(x−1)+a
x+sin(x−1)−1
o 1−x
1−√x = 1/4.</p>
Step-by-Step Solution
Key Concept: General
<p><strong>1</strong>: Exponent \to 2. Base \to (1 -a)/2.</p><p><strong>2</strong>: ((1 -a)/2)2 = 1/4 =\Rightarrow |1 -a| = 1 =\Rightarrow a = 0, 2.</p><p><strong>3</strong>: Base must be positive for real power function context. a = 0 is the only non-negative</p> integer. (Note: a = 2 gives base -1/2).
Correct Answer: (0)