Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>Let [x] denote the greatest integer function. Find limx→0
tan(π sin2 x)+(|x|−sin |x|)[x]2
x2
:</p>
Step-by-Step Solution
Key Concept: General
<p><strong>1</strong>: RHL (x \to 0+): [x] = 0. Limit = \lim_{x \to 0+} tan(\pi sin2 x)</p> x2 = \pi.<p><strong>2</strong>: LHL (x \to 0-): [x] = -1. Limit = \lim_{x \to 0-tan(\pi} sin2 x)+(|x|-sin |x|)</p> x2 = \pi.
Correct Answer: (4)