Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>Match functions with: not cont, cont not diff, diff not cont-derivative, diff with cont-derivative.</p>
P→2,Q→3,R→1,S→4
P→4,Q→1,R→2,S→3
P→4,Q→2,R→1,S→3
P→2,Q→1,R→4,S→3
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>f₁=sin√(1-e^{-x²}): diff at 0. f₂=|sinx|/tan⁻¹x: cont not diff. f₃=[sin(log(x+2))]: depends on value at 0. f₄=x²sin(1/x): diff, derivative not continuous. Answer key (D): P→2,Q→1,R→4,S→3. <strong>Answer: (D)</strong></p><div class="key-concept"><strong>Key Concept:</strong> Systematically check each function at x=0</div></div>
Correct Answer: 4