limx→0(1+x)1/x−ex= - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
$- e / 2$
B
$e / 2$
C
1
D
$\frac{2}{e}$

Solution:

$\lim_{x \to 0} \frac{e (1 - \frac{x}{2} + \frac{11}{24} x^{2} . . . . . .) - e}{x} = \lim_{x \to 0} \frac{e x (- \frac{1}{2} + \frac{11}{24} x . . . .)}{x} = \frac{- e}{2}$ $(\sin c e {(1 + x)}^{\frac{1}{x}} = e (1 - \frac{x}{2} + \frac{11}{24} x^{2} . . . .))$

$\lim_{x \to 0} \frac{{(1 + x)}^{1 / x} - e}{x} =$

Solution:

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