If fx-xsin1x- x - 0 is continuous at x-0- then the value of f 0 is

Given : f(x)=xsin(1x), x0 At x=0, L.H.L.=lim_h→0f(0 h)=lim_h→ 0 ( h)sin( 1h) =0×finite=0 Since f(x) is nbsp;continuous at x=0, ⇒ nbsp; L.H.L.=f(0)=0 ∴ f(0)= ...

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Standard XII

Mathematics

Single Point Continuity

If fx=xsin1x,...

Question

If $f (x) = x sin (\frac{1}{x}), x \neq 0$ is continuous at $x = 0,$ then the value of $f (0)$ is

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Solution

The correct option is B $0$
Given : $f (x) = x sin (\frac{1}{x}), x \neq 0$
At $x = 0,$
$L . H . L . = lim h \to 0 f (0 - h) = lim h \to 0 (- h) sin (\frac{- 1}{h})$
$= 0 \times finite = 0$
Since $f (x)$ is continuous at $x = 0,$
$\Rightarrow L . H . L . = f (0) = 0$
$∴ f (0) = 0$

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Single Point Continuity

Standard XII Mathematics

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If f(x)=xsin(1x),x≠0 is continuous at x=0, then the value of f(0) is

The correct option is B 0Given : f(x)=xsin(1x), x≠0 At x=0, L.H.L.=limh→0f(0−h)=limh→0 (−h)sin(−1h) =0×finite=0 Since f(x) is continuous at x=0, ⇒L.H.L.=f(0)=0 ∴f(0)=0

If $f (x) = x sin (\frac{1}{x}), x \neq 0$ is continuous at $x = 0,$ then the value of $f (0)$ is

The correct option is B $0$
Given : $f (x) = x sin (\frac{1}{x}), x \neq 0$
At $x = 0,$
$L . H . L . = lim h \to 0 f (0 - h) = lim h \to 0 (- h) sin (\frac{- 1}{h})$
$= 0 \times finite = 0$
Since $f (x)$ is continuous at $x = 0,$
$\Rightarrow L . H . L . = f (0) = 0$
$∴ f (0) = 0$