For Lim _ x 8 , , x - 10 10 - x (where denotes fractional part fu… - Vidyadip

MCQ

For $\mathop {Lim}\limits_{x \to 8} \,\,\frac{{\sin \{ x - 10\} }}{{\{ 10 - x\} }}$ (where { } denotes fractional part function)

A
$LHL$ exist but $RHL$ does not exist
✓
$RHL$ exist but $LHL$ does not exist.
C
neither $LHL$ nor $RHL$ does not exist
D
both $RHL$ and $LHL$ exist and equals to $1$

✓

Answer

Correct option: B.

$RHL$ exist but $LHL$ does not exist.

b
$\mathop {Lim}\limits_{x \to {8^ + }} \,\,\frac{{\sin \{ x\} }}{{\{ - x\} }}$ $= 0$ as ${I + x } = {x}$ ; as $\mathop {Lim}\limits_{x \to {I^ + }} \,\,\{ x\} \, \to 0$ and$\mathop {Lim}\limits_{x \to {I^ - }} \,\,\{ - x\} \, \to 1$
$\mathop {Lim}\limits_{x \to {8^ - }} \,\,\frac{{\sin \{ x\} }}{{\{ - x\} }}$ $\to \,\, \infty $ as $sin\{x\} \to \,\, sin(1)$ and $ \{-x\} \to \,0 $

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