Question

Calculate the limit of
Xn=sin sqrt(n+1)−sin sqrt (n), n→∞

Answer 1

Xn=sin sqrt(n+1)−sin sqrt (n), n→∞

Infinity +1 is still infinity. The 1 really doesn't matter. Sqrt of infinity is still infinity. so then you have sin(infinity)-sin(infinity), which cancels out to zero.

Answer 2

Does that help?

Answer 3

Thank you.

Answer 4

While the answer is zero in this case the reasoning is not sound.