Evaluate $\lim_{n\to\infty} n^2(1-\cos\frac{x}{n})$ Find this limit by utilizing Lagrange Remainder Theorem:
$$\lim_{n\to\infty} n^2\left(1-\cos\frac{x}{n} \right)$$
I have tried using the definition and can't get it. 

use $$1-\cos{x}=2\sin^2{\dfrac{x}{2}}\approx \dfrac{x^2}{2}$$
so
$$1-\cos{\dfrac{x}{n}}\approx \dfrac{x^2}{2n^2}$$
