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## Homework Statement

**(Squeeze Principle)**Suppose

*f*,

*g*, and

*h*are real-valued functions on a neighborhood of

**a**(perhaps not including the point

**a**itself). Suppose

*f*(

**x**) ≤

*g*(

**x**) ≤

*h*(

**x**) for all

**x**and lim

_{x→a}

*f*(

**x**) =

*l*= lim

_{x→a}

*h*(

**x**). Prove that lim

_{x→a}

*g*(

**x**) =

*l*. (Hint: Given ε > 0, show that there is δ > 0 so that whenever 0 < ||

**x**-

**a**|| < δ, we have -ε <

*f*(

**x**) -

*l*≤

*g*(

**x**) -

*l*≤

*h*(

**x**) -

*l*< ε.)

**2. The attempt at a solution**

I don't understand the definition of a limit with ε and δ. The question confuses me, frankly, and I don't have any idea where I would begin. Could anyone help me understand this?