Squeezing f(x) Between g(x) and h(x): Cos, Sin, & Tan

[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??

 

[fr33pl4gu3]

solve the problem!

 

[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

 

[HallsofIvy]

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"!)