JEE Mains · Maths · STD 11 - 12. limits
Let \([x]\) denote the greatest integer less than or equal to \(x\) Then \(\mathop {\lim }\limits_{x \to 0} \,\frac{{\tan \,(\pi \,{{\sin }^2}\,x) + \,{{(\left| x \right|\, - \,\sin \,(x\,[x]))}^2}}}{{{x^2}}}\)
- A does not exist
- B equals \(\,\,\pi \)
- C equals \(\,\,\pi \,+\,1\)
- D equals \(\,\,0\)
Answer & Solution
Correct Answer
(A) does not exist
Step-by-step Solution
Detailed explanation
\(\mathop {Lt}\limits_{x \to 0} \frac{{\tan \left( {\pi {{\sin }^2}x} \right)}}{{\pi {{\sin }^2}x}}.\frac{{\pi {{\sin }^2}x}}{{{x^2}}} + {\left( {\frac{{\left| x \right| - \sin \left( {x\left[ x \right]} \right)}}{{\left| x \right|}}} \right)^2}\)…
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