Let `[.]` represent the greatest integer function and `f (x)=[tan^2 x]

1.	Let `[.]` represent the greatest integer function and `f (x)=[tan^2 x]` then :
Answer» Correct Answer - B Given, f(x) = `[tan^(2) x]` Now, ` - 45^(@) lt x lt 45^(@) ` `rArr" " tan (-45^(@)) lt tan x lt tan (45^(@))` ` rArr" "-tan 45^(@) lt tan x lt tan (45^(@))` `rArr" " 0 lt tan^(2) x lt 1` `rArr " "[tan^(2) x] = 0` i.e. f(x) is zero for all values of x from ` x =- 45^(@) to 45^(@)`. Thus, f(x) exists when ` x to 0 ` and also it is continuous at x = 0. Also, f(x) is differentiable at x = 0 and has a value of zero. Therefore, (b) is the answer.

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