Question

lim (x+1)sin(4/x) x-> infinity

Answer 1

\[\lim_{x->\infty} (x+1)\sin(\frac{4}{x})\]

You divide and multiply for sin(4/x)



\[\lim_{x->\infty} \frac{4x+4}{x} \frac{\sin(\frac{4}{x})}{\frac{4}{x}}\]

The second goes to 0 and usuing senx/x you know it goes to one.
You factorize four up there, getting...

\[1 * \lim_{x->\infty} \frac{4(x+1)}{x} \]

4 is a constant, you take it outside the limit. Everything goes at one, you have the four outside, so you have

\[\lim_{x->\infty} (x+1)\sin(\frac{4}{x}) = 4\]

Answer 2

Thanks!

Answer 3

You're welcome :)