Find-lim-x-sin-x-x-

Question Number 52123 by 786786AM last updated on 03/Jan/19

Find \lim_{x \to \infty} \frac{\sin x}{x} .

Commented by turbo msup by abdo last updated on 03/Jan/19

w e h a v e ∣ \frac{s i n x}{x} ∣⩽ \frac{1}{∣ x ∣} \forall x \neq 0 \Rightarrow

{l i m}_{x - \to \bar{+} \infty} \frac{s i n x}{x} = 0

Answered by tanmay.chaudhury50@gmail.com last updated on 03/Jan/19

t = \frac{1}{x}

\lim_{t \to 0} t s i n (\frac{1}{t})

f o r a n y v a l u e o f t, t h e v a l u e o f s i n (\frac{1}{t}) o s c i l l a t e s

b e t w e e n \pm 1 s o

\lim_{t \to 0} t \times \lim_{t \to 0} s i n (\frac{1}{t})

= 0 \times (\pm 1)

= 0

i a m a t t a c h i n g g r a p h f o r t h e s a m e \dots

Commented by tanmay.chaudhury50@gmail.com last updated on 03/Jan/19

Commented by tanmay.chaudhury50@gmail.com last updated on 03/Jan/19