The value of limx - 0-x-x-x- sin-x-x- is where - is greatest integer function

Given : L= lim_x → 0 ^ x([x] + |x|) sin[x]|x| = lim_h→0(0 h)([0 h] + |0 h|) sin[0 h]|0 h| = lim_h → 0( h)( 1 +h)sin( 1)h = lim_h → 0 (1 h)sin11 = sin 1 ...

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Standard XII

Mathematics

Single Point Continuity

The value of ...

Question

The value of $lim x \to 0^{-} \frac{x ([x] + | x |) sin [x]}{| x |}$ is
(where $[.]$ is greatest integer function)

sin 1

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- sin 1

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Solution

The correct option is C $- sin 1$
Given :
$L = lim x \to 0^{-} \frac{x ([x] + | x |) sin [x]}{| x |}$
$= lim h \to 0 \frac{(0 - h) ([0 - h] + | 0 - h |) sin [0 - h]}{| 0 - h |}$
$= lim h \to 0 \frac{(- h) (- 1 + h) sin (- 1)}{h}$

$= lim h \to 0 - \frac{(1 - h) sin 1}{1}$
$= - sin 1$

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Single Point Continuity

Standard XII Mathematics

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The value of limx→0−x([x]+|x|)sin[x]|x| is (where [.] is greatest integer function)

The correct option is C −sin1Given : L=limx→0 −x([x]+|x|)sin[x]|x| =limh→0(0−h)([0−h]+|0−h|)sin[0−h]|0−h| =limh→0(−h)(−1+h)sin(−1)h =limh→0−(1−h)sin11 =−sin1

The value of $lim x \to 0^{-} \frac{x ([x] + | x |) sin [x]}{| x |}$ is
(where $[.]$ is greatest integer function)

The correct option is C $- sin 1$
Given :
$L = lim x \to 0^{-} \frac{x ([x] + | x |) sin [x]}{| x |}$
$= lim h \to 0 \frac{(0 - h) ([0 - h] + | 0 - h |) sin [0 - h]}{| 0 - h |}$
$= lim h \to 0 \frac{(- h) (- 1 + h) sin (- 1)}{h}$

$= lim h \to 0 - \frac{(1 - h) sin 1}{1}$
$= - sin 1$