# Limit help.

• Nov 27th 2011, 05:48 AM
Fabio010
Limit help.
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"
• Nov 27th 2011, 06:24 AM
skeeter
Re: Limit help.
Quote:

Originally Posted by Fabio010
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"

as x gets closer to 0, $\displaystyle \frac{1}{3\pi \cdot x}$ becomes a very large value ... yet, $\displaystyle -1 \le \cos(any \, value) \le 1$

so, what you have is ...

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

understand why the limit is 0?
• Nov 27th 2011, 06:59 AM
Fabio010
Re: Limit help.
Understood.

Thanks for the help.!
• Nov 27th 2011, 10:17 PM
CaptainBlack
Re: Limit help.
Quote:

Originally Posted by Fabio010
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"

Squeeze theorem:

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

CB