Finding a limit when assigned restrictions to f(x)

[thatguythere]

Homework Statement

Suppose 0 ≤ f(x) ≥ 1 for all x, find lim x→0 x^4f(x)

Homework Equations

The Attempt at a Solution

I'm very uncertain about how to go about doing this.
lim x→0 x^4 f(x) = 0^4 (0)
= 0
lim x→0 x^4 f(x) = 1^4 (1)
=1
How does that prove anything?

 

[Mark44]

Homework Statement

Suppose 0 ≤ f(x) ≥ 1 for all x, find lim x→0 x^4f(x)

Don't you mean 0 ≤ f(x) ≤ 1?

Have you learned the "squeeze" theorem?

Homework Equations

The Attempt at a Solution

I'm very uncertain about how to go about doing this.
lim x→0 x^4 f(x) = 0^4 (0)
= 0
lim x→0 x^4 f(x) = 1^4 (1)
=1
How does that prove anything?