find-lim-x-gt-0-1-sinx-1-x-

Question Number 27789 by abdo imad last updated on 14/Jan/18

f i n d {l i m}_{x - > 0} {(1 + s i n x)}^{\frac{1}{x}} .

Commented by abdo imad last updated on 15/Jan/18

w e h a v e {(1 + s i n x)}^{\frac{1}{x}} = e^{\frac{1}{x} l n (1 + s i n x)}

b u t f o r x \in V (0) s i n x \sim x a n d

l n (1 + s i n x) \sim l n (1 + x) \sim x \Rightarrow

\frac{l n (1 + s i n x)}{x} \sim 1 \Rightarrow {l i m}_{x - > 0} {(1 + s i n x)}^{\frac{1}{x}} = e .

Commented by prakash jain last updated on 16/Jan/18

thanks . your question and solution

are great learning experience

Commented by abdo imad last updated on 16/Jan/18

t h s n k y o u f r i e n d p r a k a s h \dots