Calculate-1-lim-x-0-x-1-2x-1-x-2-lim-x-a-sin-x-sin-a-1-x-a-

Question Number 160900 by LEKOUMA last updated on 08/Dec/21

C a l c u l a t e

1) \lim_{x \to 0} {(\frac{x + 1}{2 x + 1})}^{x^{2}}

\lim_{x \to a} {(\frac{\sin x}{\sin a})}^{\frac{1}{x - a}}

Commented by cortano last updated on 09/Dec/21

(1) = 1

(2) = e^{\lim_{x \to a} \frac{\sin x - \sin a}{x - a}} = e^{\cos a}

Commented by stelor last updated on 11/Dec/21

1) 1

2) l = \lim_{x \to a} e^{\frac{\ln (s i n x) - l n (s i n a)}{x - a}}

l n (l) = {[l n (s i n x)]}_{a}^{'} = c o \tan (a)

l = e^{c o t a n (a)}

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