A point where function f (x) = [sin [x]] is not continuous in (0, 2π), [.] denotes the greatest integer le x, is

Question

A point where function f (x) = [sin [x]] is not continuous in (0, 2π), [.] denotes the greatest integer le x, is (A) (3, 0) (B) (2, 0) (C) (1, 0) (D) none of these

Tardigrade Admin · Accepted Answer

For 0 le x < 1, f (x)=[sin 0]=0, 1 le x < 2, f (x)=[sin 1]=0, 2 le x < 3, f (x)=[sin 2]=0, 3 le x < 4, f(x)=[sin 3]=0, 4 le x < 5, f (x)=[sin 4]=-1 Hence, there is discontinuity at point (4,-1)

Q. A point where function $f (x) = [s in [x]]$ is not continuous in $(0, 2 π)$ , [.] denotes the greatest integer $\leq x$ , is

$(3, 0)$

$(2, 0)$

$(1, 0)$

none of these

For
$0 \leq x < 1, f (x) = [s in 0] = 0$ ,
$1 \leq x < 2, f (x) = [s in 1] = 0$ ,
$2 \leq x < 3, f (x) = [s in 2] = 0$ ,
$3 \leq x < 4, f (x) = [s in 3] = 0$ ,
$4 \leq x < 5, f (x) = [s in 4] = - 1$
Hence, there is discontinuity at point $(4, - 1)$

Q. A point where function f(x)=[sin[x]] is not continuous in (0,2π), [.] denotes the greatest integer ≤x, is

(3,0)

(2,0)

(1,0)