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Limits Continuity and Differentiability question

2021 · 16 Mar · Shift 2 · Q35
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  5. /2021 · 16 Mar · Shift 2 · Q35

Limits Continuity and Differentiability question

2021 · 16 Mar · Shift 2 · Q35

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1
Let α∈\alpha\inα∈ R be such that the function f(x)={cos⁡−1(1−{x}2)sin⁡−1(1−{x}){x}−{x}3,xe0α,x=0f(x) = \left\{ {\begin{matrix} {{{{{\cos }^{ - 1}}(1 - {{\{ x\} }^2}){{\sin }^{ - 1}}(1 - \{ x\} )} \over {\{ x\} - {{\{ x\} }^3}}},} & {x e 0} \\ {\alpha ,} & {x = 0} \\ \end{matrix} } \right.f(x)={{x}−{x}3cos−1(1−{x}2)sin−1(1−{x})​,α,​xe0x=0​ is continuous at x = 0, where {x} = x −-− [ x ] is the greatest integer less than or equal to x. Then :
  1. A
    no such α\alphaα exists
  2. B
    α\alphaα = 0
  3. C
    α\alphaα=π4{\pi \over 4}4π​
  4. D
    α\alphaα=π2{\pi \over {\sqrt 2 }}2​π​
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