# Squeeze theorem

1. Aug 23, 2008

### fr33pl4gu3

f(x)=x4 cos(2/x6)

g(x) <= f(x) <= h(x)

how to get g(x) and h(x) by using the squeeze theorem??

I know is something like this -1 <= x <= 1

But how do i implement it here, and especially to the cos, sin, and tan??

2. Aug 23, 2008

### fr33pl4gu3

solve the problem!!

3. Aug 23, 2008

### roam

So in your question, $$x^4 . cos \frac{2}{x^6}$$ what's the limit ie. as x approaches what? zero?

Then we can use the squeezing theorem; $$g(x) \leq f(x) \leq h(x)$$
Assuming that the limit of f(x) as x approaches c is L then;

$$lim_{x \rightarrow c} g(x) = lim_{x\rightarrowc} h(x) = L$$

Thus $$lim_{x \rightarrow c} f(x) = L$$

Last edited: Aug 23, 2008
4. Aug 23, 2008

### HallsofIvy

Staff Emeritus
What exactly is the question? The "squeeze theorem" refers to limits but you are trying to find the limit of x4cos(2/x6) as x goes to what?

(And it is your responsibility to "solve the problem"!)

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