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$If f (x) = \{\begin{array}{cl} x^{α} \cos (\frac{1}{x}) & , if x \neq 0 \\ 0, & if x = 0 \end{array} is continuous at x = 0 then$

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α<0

α>0

α=0

α≥0

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detailed solution

Correct option is B

continuous when α>0

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If f(x)=xαcos⁡1x, if x≠00, if x=0 is continuous at x=0 then

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$If f (x) = \{\begin{array}{cl} x^{α} \cos (\frac{1}{x}) & , if x \neq 0 \\ 0, & if x = 0 \end{array} is continuous at x = 0 then$