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)= ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Derivative of Standard Functions

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

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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 $x = 0,$
$\Rightarrow L . H . L . = f (0) = 0$
$∴ f (0) = 0$

Suggest Corrections

Similar questions

Q. If

f (x) = \frac{2 - \sqrt{x + 4}}{\sin 2 x}, x \neq 0,

is continuous at x = 0, then f(0) = ______________.

Q. If

f (x) = \frac{2 x + 3 \sin x}{3 x + 2 \sin x},

x ≠ 0 is continuous at x = 0, then find f (0).

Q. If

f (x) = {x sin \frac{1}{x}, x \neq 0 k, x = 0}

is continuous at

x = 0

, then the value of

k

Q. If function

f (x) = ⎧ ⎨ ⎩ \begin{matrix} x sin (\frac{1}{x}); x \neq 0 a; x = 0 \end{matrix}

is continuous at

x = 0

, then the value of

a

Q. If

f (x) = x sin \frac{1}{x}, x \neq 0

then the value of the function at

x = 0

so that the function is continuous at

x = 0

is-

Join BYJU'S Learning Program

Explore more

Derivative of Standard Functions

Standard XII Mathematics

Join BYJU'S Learning Program

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 $x = 0,$
$\Rightarrow L . H . L . = f (0) = 0$
$∴ f (0) = 0$