Limits, Continuity & Differentiability
General
Grade None
Question:
<p><span class="math-inline">\(f(x)=\begin{cases}\pi/4+\tan^{-1}x & |x|\ge 1\\ \frac{1}{2}(|x|-1) & |x|<1\end{cases}\)</span>. f is:</p>
<strong>cont ℝ-{1}, diff ℝ-{-1,1}</strong>
cont & diff ℝ-{-1}
cont ℝ-{-1}, diff ℝ-{-1,1}
cont & diff ℝ-{1}
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>At x=1: left limit=0, right limit=π/2. Discontinuous at x=±1. Differentiable on ℝ-{-1,1}. <strong>Answer: (1)</strong></p><div class="key-concept"><strong>Key Concept:</strong> Check each junction for continuity first</div></div>
Correct Answer: 1