Question

Find the limit.

Answer 1

\[\lim_{x \rightarrow \infty} \frac{ 1 }{ 2x+ sinx }\]

Answer 2

\[2x-1\le2x+\sin(x)\le2x+1\]

so for \(x\) large



\[\frac{1}{2x-1}\ge\frac{1}{2x+\sin(x)}\ge\frac{1}{2x+1}\]

Answer 3

There is no limit, because the value does NOT converge.

Answer 4

it does converge

Answer 5

I think the limie is 0
\[\frac{1}{\infty \pm 1} => \frac{1}{\infty} => 0\]

Answer 6

oh, whoops. I see it now. ignore what i said earlier lol