Limits, Continuity & Differentiability
General
Grade None
Question:
<p>Let f(x) =
(
1 + 2x
a
0 ≤x < 1
ax
1 ≤x < 2. If limx→1 f(x) exists, then the value(s) of a is:</p>
Step-by-Step Solution
Key Concept: General
<p><strong>1</strong>: LHL = \lim_{x \to 1-1} + 2x</p> a = 1 + 2 a.<p><strong>2</strong>: RHL = \lim_{x \to 1+} ax = a.</p><p><strong>3</strong>: Equating LHL and RHL: 1 + 2</p> a = a =\Rightarrow a + 2 = a2.<p><strong>4</strong>: a2 -a -2 = 0 =\Rightarrow (a -2)(a + 1) = 0. Thus a = 2, -1.</p>
Correct Answer: (B, C)