Find limit LIM (x tends to infinity) [(x + 1) ^ (x + 1) / x ^ x] sin (1 / x)

Find limit LIM (x tends to infinity) [(x + 1) ^ (x + 1) / x ^ x] sin (1 / x)

sin(1/x)~1/x,
So that formula becomes (1 + 1 / x) ^ (x + 1),
And then into an exponential function, with the law of lobita, so that the landlord understand Bai?
If you don't, ask,