Question

i hope you will give me a solution​

Answer 1

Answer:

$\sf \large \: \green{Option \: (c) \: e}$

Step-by-step explanation:

$\displaystyle \sf \: \lim_{n\to \: \infty } \bigg( \bigg(1 + \frac{1}{n} \bigg)^{n} \bigg)$

Common limit.

$\sf \: e^{1}$

$\green{ \boxed{ \green{\sf \implies \: e}}}$

Additional information:

$\displaystyle \sf\lim_{x \to \: a} \frac{ {x}^{n} - {a}^{n} }{x - a} = na {}^{n - 1}$

$\displaystyle \sf \lim_{x \to \: 0} \frac{ \tan(x) }{x} = 1$

$\displaystyle \sf \lim_{x \to \: 0} \frac{ \sin(x) }{x} = 1$

$\displaystyle \sf \lim_{x \to \: a} \frac{ \sin(x - a) }{x - a} = 1$