JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(\alpha \in R\) be such that the function \(f(x)=\left\{\begin{array}{ll} \frac{\cos ^{-1}\left(1-\{x\}^{2}\right) \sin ^{-1}(1-\{x\})}{\{x\}-\{x\}^{3}}, & x \neq 0 \\ \alpha, & x=0 \end{array}\right.\) is continuous at \(x=0,\) where \(\{x\}=x-[x],[x]\) is the greatest integer less than or equal to \(X\). Then :
- A \(\alpha=\frac{\pi}{\sqrt{2}}\)
- B \(\alpha=0\)
- C no such \(\alpha\) exists
- D \(\alpha=\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(C) no such \(\alpha\) exists
Step-by-step Solution
Detailed explanation
\(\operatorname{Lim}_{x \rightarrow 0^{+}} f(x)=f(0)=\operatorname{Lim}_{x \rightarrow 0^{-}}(x)\) \(\operatorname{Lim}_{x \rightarrow 0^{+}} \frac{\cos ^{-1}\left(1-x^{2}\right) \cdot \sin ^{-1}(1-x)}{x(1-x)(1+x)}\)…
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