Let [t] denote the greatest integer le t displaystyle limx → 0 x[(4/x)]=A. Then the function. and f (x)=[x2]sin(π x) is discontinuous, when x is equal to :

Question

Let [t] denote the greatest integer le t displaystyle limx → 0 x[(4/x)]=A. Then the function. and f (x)=[x2]sin(π x) is discontinuous, when x is equal to : (A) √A+1 (B) √A (C) √A+5 (D) √A+21

Tardigrade Admin · Accepted Answer

A = displaystyle limx→0 x [(4/x)] = displaystyle lim x→ 0 x [(4/x)]-x (4/x) = 4 Æ(x) = [x2]sin(π x) will be discontinuous at nonintegers ∴ x = √A+1 i.e. √5

Q. Let $[t]$ denote the greatest integer $\leq t$ $x \to 0 lim$ $x [\frac{4}{x}] = A .$ Then the function. and $f (x) = [x^{2}] s in (π x)$ is discontinuous, when $x$ is equal to :

$A + 1$

$A$

$A + 5$

$A + 21$

$A = x \to 0 lim x [\frac{4}{x}] = x \to 0 lim x [\frac{4}{x}] - x {\frac{4}{x}} = 4$
$ƒ (x) = [x^{2}] s in (π x)$ will be discontinuous at nonintegers
$∴ x = A + 1 i . e . 5$

Q. Let [t] denote the greatest integer ≤t x→0lim​ x[x4​]=A. Then the function. and f(x)=[x2]sin(πx) is discontinuous, when x is equal to :

A+1​

A​

A+5​

A+21​

A=x→0lim​x[x4​]=x→0lim​x[x4​]−x{x4​}=4 ƒ(x)=[x2]sin(πx) will be discontinuous at nonintegers ∴x=A+1​i.e.5​

Q. Let $[t]$ denote the greatest integer $\leq t$ $x \to 0 lim$ $x [\frac{4}{x}] = A .$ Then the function. and $f (x) = [x^{2}] s in (π x)$ is discontinuous, when $x$ is equal to :

$A + 1$

$A$

$A + 5$

$A + 21$

$A = x \to 0 lim x [\frac{4}{x}] = x \to 0 lim x [\frac{4}{x}] - x {\frac{4}{x}} = 4$
$ƒ (x) = [x^{2}] s in (π x)$ will be discontinuous at nonintegers
$∴ x = A + 1 i . e . 5$