X sinfrac1x- x neq 0 10 - x-0A- 1B- 0C- -1D- does not exist

The correct option is B 0 Here f(0)=0 Since 1 ≤ sin 1/x ≤ 1 ⇒ |x| ≤ xsin 1/x ≤ |x| We know that lim_x→ 0 |x| = 0 and lim_x→ 0 |x|=0 In this way lim_x→ 0 f ...

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Standard XI

Mathematics

L'Hospital Rule to Remove Indeterminate Form

x sinfrac1x& ...

Question

$If f (x) = {\begin{matrix} x s i n \frac{1}{x} & x \neq 0 0 & x = 0 \end{matrix}, then lim x \to 0 f (x) =$

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-1

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does not exist

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Solution

The correct option is B
0

Here f(0)=0
Since -1 ≤ sin $\frac{1}{x}$ ≤ 1 ⇒ -|x| ≤ xsin $\frac{1}{x}$ ≤ |x|

We know that $l i m_{x \to 0}$ |x| = 0 and $l i m_{x \to 0}$ - |x|=0

In this way $l i m_{x \to 0}$ f(x) =0

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Similar questions

Q. If

f (x) = ⎧ ⎨ ⎩ \begin{matrix} \frac{sin [x]}{[x]}, & [x] \neq 0 0, & [x] = 0 \end{matrix},

where [x] denotes the greatest integer less than or equal to x then

lim x \to 0 f (x)

equals

$l i m_{x \to 0} \frac{(e^{1 / x} - 1)}{(e^{1 / x}) + 1}$

If $f (x) = x s i n (\frac{1}{x}), x \neq 0,$ then ${lim}_{x \to 0} f (x) =$

Q. If

f (x) = x \sin (1 / x), x \neq 0,

then

\lim_{x \to 0} f (x) =

(a) 1
(b) 0
(c) −1
(d) does not exist

Q. The value of

lim x \to 0^{+} [x sin (\frac{1}{x}) + (sin x)^{1 / x} + {(\frac{1}{x})}^{sin x}],

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If f(x)={xsin1xx≠00x=0,then limx→0 f(x)=

The correct option is B 0 Here f(0)=0 Since -1 ≤ sin 1x ≤ 1 ⇒ -|x| ≤ xsin 1x ≤ |x| We know that limx→0 |x| = 0 and limx→0 - |x|=0 In this way limx→0 f(x) =0

$If f (x) = {\begin{matrix} x s i n \frac{1}{x} & x \neq 0 0 & x = 0 \end{matrix}, then lim x \to 0 f (x) =$

The correct option is B
0

Here f(0)=0
Since -1 ≤ sin $\frac{1}{x}$ ≤ 1 ⇒ -|x| ≤ xsin $\frac{1}{x}$ ≤ |x|

We know that $l i m_{x \to 0}$ |x| = 0 and $l i m_{x \to 0}$ - |x|=0

In this way $l i m_{x \to 0}$ f(x) =0