What is the limit of:

lim $\displaystyle \pi x cos(\frac{1}{3 \pi x})$

x->0

My teacher said that what is inside of cosine is limited so $\displaystyle cos(\frac{1}{3 \pi x})$[TEX] it doesnt "metter"...

and limit when$\displaystyle x -> 0$ = $\displaystyle \pi 0 = 0 $

Can you explain me why the it "doesnt metter"