Let y = f(x) be defined in [a, b], then
(i) Test of continuity at `x = c, a lt c lt b`
(ii) Test of continuity at x = a
(iii) Test of continuity at x = b
Case I Test of continuity at `x = c, a lt c lt b`
If y = f(x) be defined at x = c and its value f(c) be equal to limit of f(x) as `x rarr c` i.e. f(c) = `lim_(x rarr c) f(x)`
or `lim_(x rarr c^(-))f(x) = f(c) = lim_(x rarr c^(+)) f(x)`
or LHL = f(c) = RHL
then, y = f(x) is continuous at x = c.
Case II Test of continuity at x = a
If RHL = f(a)
Then, f(x) is said to be continuous at the end point x = a
Case III Test of continuity at x = b, if LHL = f(b)
Then, f(x) is continuous at right end x = b.
If `f(x) = {{:(sin x",",x le 0),(tan x",",0 lt x lt 2pi),(cos x",",2pi le x lt 3pi),(3pi",",x = 3pi):}`, then f(x) is discontinuous at

Options

A. `(pi)/(2),(3pi)/(2),2pi,3pi`
B. `0, (pi)/(2),pi,(3pi)/(2), 3pi`
C. `(pi)/(2), 2pi`
D. None of these

Answer

A