Question

Plz help! Evaluate the limit of the following. (1/n)(sin(n*pi/2))

Answer 1

$\frac{\pi}{2}$

Step-by-step explanation:

When $n->$0 ,$\frac{Sin(kn)}{n}->k$

This is because,

using l'hospital's rule,$Lt_{n->0}\frac{sin(kn)}{n}=\frac{kcos(n)}{1} =\frac{k\times 1}{1} =k$

In the given question,$k=\frac{n\times\pi}{2}$

So,the given limit evaluates to $\frac{n\pi}{2}$