Question:
Evaluate
limₓ\to0√((x-sin x)/(x+sin² x))
Evaluate
limₓ\to0√((x-sin x)/(x+sin² x))
Show Hint
Use series expansions for limits involving trig functions.
Updated On: Mar 20, 2026
- \(1\)
- \(0\)
- \(\infty\)
- None of these
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The Correct Option is B
Solution and Explanation
Step 1: Use expansions: sin x=x-(x³)/(6)+⋯
Step 2: Then x-sin x~ (x³)/(6), x+sin²x~ x+x²
Step 3: (x-sin x)/(x+sin²x)~(x³)/(6x)= (x²)/(6)
Step 4: √((x²)/(6))\to0
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