Question

please solve this question of limit​

Answer 1

${ \bold{ \green{ \huge{ \underline{ ANSWER } : - }}}} \\ \\ { \bold{ \underline{ Given } : - }} \\ \\ { \bold{ \blue{ \implies \: lim_{x - > 1}(1 - x) \tan( \frac{\pi \: x}{2} ) }}}$

${ \bold{ \huge{ \mathfrak{ \red{solution : - }}}}} \\ \\ { \bold{ { \blue{\implies \:given \: \: form \: \: of \: \: limit \: \: is \: \: 0 \times \infty \: \: and }}}} \\ { \bold{ { \blue{ \: \: \: \: \: \: \: \: \: \: \: \: \: its \: \: called \: \: undefinded \: \: form}}}} \\ \\ { \bold{ { \blue{ = \: lim_{x - > 1} (\frac{1 - x}{\cot( \frac{\pi \: x}{2} )}) }}}} \\ \\ { \bold{ { \blue{\implies \: now \: \: its \: \: \frac{0}{0} \: \: form \:, \: so \: we \: \: can \: \: use \: \:L'HOSPITAL \: \: rule - }}}} \\ \\ { \bold{ { \blue{ = \: lim_{x - > 1}( \frac{ - 1}{ - {cosec}^{2}( \frac{\pi \: x}{2} ) \times \frac{\pi}{2} } ) }}}} \\ \\ { \bold{ \blue{ = \frac{1}{ {cosec}^{2}( \frac{\pi}{2} ) \times \frac{\pi}{2} } = \frac{2}{\pi} }}} \\ \\ \\ { \bold{ { \boxed{ \boxed{ \red{ \huge \mathbb{ANSWER = \frac{2}{\pi} }}}}}}}$

Answer 2

Answer:

2/π

Step-by-step explanation:

solution is in above attached