Question

How are these equal?
\[\lim_{x \rightarrow \infty}\frac{\sin(1/x)}{1/x}=\lim_{\theta \rightarrow 0}\frac{\sin \theta}{\theta}=1\]

Answer 1

I know that lim sinx/x as x-> 0 is 1, but im not sure how the leftmost part becomes equal to the right part

Answer 2

let \[\theta=\frac{1}{x}\]

Answer 3

how does the limit go from infinity to 0?

Answer 4

tha's the part i'm having trouble with ._.

Answer 5

if \[x\to \infty\text{ then }\frac{1}{x}\to 0\]

Answer 6

ohh.. right =_= omg I feel so dumb lol. Thanks :D