Continuity Proof: f(x) = x^3 [cos(pi/x^2) + sin(pi/x^2)]

[JPanthon]

Homework Statement

f(x) = x^3 [cos(pi/x^2) + sin(pi/x^2)] for x≠0

Homework Equations

The Attempt at a Solution

I really am stuck.

I've tried squeeze theorem on [cos(pi/x^2) + sin(pi/x^2)], but I can't compute the range.

So, I tried doing it individually, squeezing -1 ≤ cos(pi/x^2) ≤ 1, but that doesn't work.

Any hints please?

 

[SammyS]

cos(θ)+sin(θ) = (√2)sin(θ + π/4)

 

[Matterwave]

What's the question exactly? You want to prove that that function is continuous?

 

[HallsofIvy]

The given function is obviously continuous for $x\ne 0$ because it is a composition of continuous functions. It obviously not continuous for x= 0 because it is not defined at x= 0.

Because I suspect the problem was not supposed to be that "obvious", please check again and tell us what the problem really is!