For a real number y, let [y] denotes the greatest integer… — JEE Main 1981 Mathematics PYQ

1981

For a real number

y

, let

[y]

denotes the greatest integer less than or equal to

y

. Then, the function

f(x) = \dfrac{\tan \pi\, [(x-\pi)]}{1+[x]^2}

is \\

A.
discontinuous at some $x$
B.
continuous at all $x$ , but the derivative $f'(x)$ does not exist for some $x$
C.
$f'(x)$ exists for all $x$ , but the derivative $f''(x)$ does not exist for some $x$
D.
$f'(x)$ exists for all $x$

Show answer

Correct option: D

[1981]

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JEE Main 1981 Mathematics question on Limits Continuity and Differentiability