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  • Let [] denote the greatest integer function and  , then :

Let [] denote the greatest integer function and \mathrm{f(x)=\left[\tan ^2 x\right]} , then :

Option: 1

\mathrm{\lim _{x \rightarrow 0} f(x) \text { does not exist. } }


Option: 2

f(x) \text { is continuous at } x=0 \text {. }


Option: 3

f(x) \text { is not differentiable at } x=0 \text {. }


Option: 4

f^{\prime}(0)=1 .


Answers (1)

best_answer

\mathrm{0 \leq \tan ^2 x<1 \text { when }-\frac{\pi}{4}<x<\frac{\pi}{4}}
\mathrm{\Rightarrow f(x)=0,-\frac{\pi}{4}<x<\frac{\pi}{4}}
\mathrm{\text { Hence, } f(x) \text { is continuous and differentiable at } x=0 \text {, also, } f^{\prime}(0)=0 \text {. }}

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