Question

5.
1
lim,-- sin
is equal to
1
1
question in pic
if you type anything u will be reported​

Answer 1

Step-by-step explanation:

We have,

$\lim _{x \rarr1} \sin(x - \frac{1}{ {x}^{ \frac{1}{3} } - 1} )$

$= \sin \{ \lim _{x \rarr1}(x - \frac{1}{ {x}^{ \frac{1}{3} } - 1} )\}$

$= \sin \{ \lim _{x \rarr1}( \frac{ {x}^{ \frac{4}{3} } - x - 1 }{ {x}^{ \frac{1}{3} } - 1} )\}$

Using l'hospital's rule,

$= \sin \{ \lim _{x \rarr1}( \frac{ \frac{4}{3} {x}^{ \frac{1}{3} } - 1 }{ \frac{1}{3} {x}^{ - \frac{2}{3} } } )\}$

$= \sin \{ \frac{ \frac{4}{3}- 1 }{ \frac{1}{3} }\}$

$= \sin \{ \frac{ \frac{4 - 3}{3}}{ \frac{1}{3} }\}$

$= \sin \{ \frac{ \frac{1}{3}}{ \frac{1}{3} }\}$

$= \sin \{1\}$