# Thread: Limit help.

1. ## Limit help.

What is the limit of:

lim $\pi x cos(\frac{1}{3 \pi x})$
x->0

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

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

Can you explain me why the it "doesnt metter"

2. ## Re: Limit help.

Originally Posted by Fabio010
What is the limit of:

lim $\pi x cos(\frac{1}{3 \pi x})$
x->0

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

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

Can you explain me why the it "doesnt metter"
as x gets closer to 0, $\frac{1}{3\pi \cdot x}$ becomes a very large value ... yet, $-1 \le \cos(any \, value) \le 1$

so, what you have is ...

$\lim_{x \to 0} \pi x (some \, value \, between \, -1 \, and \, 1)$

understand why the limit is 0?

3. ## Re: Limit help.

Understood.

Thanks for the help.!

4. ## Re: Limit help.

Originally Posted by Fabio010
What is the limit of:

lim $\pi x cos(\frac{1}{3 \pi x})$
x->0

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

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

Can you explain me why the it "doesnt metter"
Squeeze theorem:

$-\pi x \le \pi x \cos\left(\frac{1}{3\pi x} \right) \le \pi x$

CB