Limits Continuity and Differentiability

JEE Main 2021 · 16 Mar, Evening shift · Q4144

MathematicsMedium179×since 2002Q4144

Let

\alpha

\in

R be such that the function

f(x) = \left\{ {\matrix{ {{{{{\cos }^{ - 1}}(1 - {{\{ x\} }^2}){{\sin }^{ - 1}}(1 - \{ x\} )} \over {\{ x\} - {{\{ x\} }^3}}},} & {x \ne 0} \cr {\alpha ,} & {x = 0} \cr } } \right.

is continuous at x = 0, where {x} = x

-

[ x ] is the greatest integer less than or equal to x. Then :

JEE Main 2021 · 16 Mar, Evening shift · Q4144

MathematicsMedium179×since 2002Q4144

Let

\alpha

\in

R be such that the function

f(x) = \left\{ {\matrix{ {{{{{\cos }^{ - 1}}(1 - {{\{ x\} }^2}){{\sin }^{ - 1}}(1 - \{ x\} )} \over {\{ x\} - {{\{ x\} }^3}}},} & {x \ne 0} \cr {\alpha ,} & {x = 0} \cr } } \right.

is continuous at x = 0, where {x} = x

-

[ x ] is the greatest integer less than or equal to x. Then :

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