If f(x)=tan[(2x−3π)3]π1+[2x−3π]2 ([.] denotes the greatest integer function), then

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f(x) is continuous in R

f(x) is continuous in R but not differentiable in R

f'(x) exists everywhere but f'(x) does not exist at some x∈R

None of these

answer is A.

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Detailed Solution

∵[(2x−3π)3]= integer (say n ) ∴ tannπ=0 And 1+[2x−3π]2≠0 Hence, f(x)=0 Hence, f(x) is continuous and differentiable for all x∈R.

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