Let \alpha \in R be such that the function f(x)=\\begin{array}{c}\\\{\cos ^{-1\end{array}(1-\{x\}^{2}) \sin ^{-1}(1-\{x\})}/{\{x\}-\{x\}^{3}}, , x \neq 0 ; \alpha, , x=0. is continuous at x=0, where \{x\}=x-[x],[x] is the greatest integer less than or equal to x. Then, [16 Mar 2021 Shift 2]

Correct Answer is : no such α exists

Limits, Continuity and Differentiability Part 2

Section: Mathematics

Question : 86 of 100

Marks: +1, -0

Let α∈R be such that the function

f(x)={

‌

cos−1(1−{x}2)sin−1(1−{x})

{x}−{x}3

‌

x≠0

‌

x=0.

is continuous at x=0, where {x}=x−[x],[x] is the greatest integer less than or equal to x. Then,

[16 Mar 2021 Shift 2]

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