Question

class 11 limits how to solve this question?

Answer 1

$\large\underline{\bold{Solution :- }}$

$\tt \:\lim_{x\to\ {0}^{ - } } \bigg(\dfrac{1}{1 + {2}^{ \frac{1}{x} } } \bigg)$

$\tt \:  ⟼Put \: x \: = 0 - h \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \tt \:  ⟼as \: x \: ⟼0\tt\implies \: \: h \: ⟼0$

$\tt \: = \lim_{h\to\ {0} } \bigg(\dfrac{1}{1 + {2}^{ \frac{1}{0 - h} } } \bigg)$

$\tt \: = \lim_{h\to\ {0} } \bigg(\dfrac{1}{1 + {2}^{ \frac{1}{ - h} } } \bigg)$

$\tt\ \: = \dfrac{1}{1 + {2}^{ - \infty \: } }$

$\tt \:  = \dfrac{1}{1 + 0}$

$\tt \:  = 1$