Let f(x)=( sin (1/4) π[x]/[x]). Then which one of the following does NOT hold good? [Note: [y] denotes greatest integer function less than or equal to y.]

Question

Let f(x)=( sin (1/4) π[x]/[x]). Then which one of the following does NOT hold good? [Note: [y] denotes greatest integer function less than or equal to y.] (A) f(x) is not continuous at any point. (B) f(x) is continuous at x=(3/2). (C) f ( x ) is discontinuous at x =2. (D) f(x) is differentiable at x=(4/3).

Tardigrade Admin · Accepted Answer

g(x)=( sin (π[x]/4)/[x]) obv. cont. at x=3 / 2 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/331a39949e1f80941bb5b11cc4460c8d-.png" /> Hence discontinuous at x = 2

Q. Let $f (x) = \frac{s i n \frac{1}{4} π [ x ]}{[ x ]}$ . Then which one of the following does NOT hold good?
[Note: $[y]$ denotes greatest integer function less than or equal to $y$ .]

$f (x)$ is not continuous at any point.

$f (x)$ is continuous at $x = \frac{3}{2}$ .

$f (x)$ is discontinuous at $x = 2$ .

$f (x)$ is differentiable at $x = \frac{4}{3}$ .

$g (x) = \frac{s i n \frac{π [ x ]}{4}}{[ x ]}$ obv. cont. at $x = 3/2$

Hence discontinuous at $x = 2$

Q. Let f(x)=[x]sin41​π[x]​. Then which one of the following does NOT hold good? [Note:[y] denotes greatest integer function less than or equal to y.]

f(x) is not continuous at any point.

f(x) is continuous at x=23​.

f(x) is discontinuous at x=2.

f(x) is differentiable at x=34​.