(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove the Squeeze theorem when x tends to -∞

2. Relevant equations

Squeeze theorem:

f, g and h defined over (a-r , r+a) r>0 [itex]\forall[/itex] x[itex]\in[/itex] (a-r , r+a)

f(x)[itex]\leq[/itex]g(x)[itex]\leq[/itex]h(x)

if lim f(x) = lim h(x) = L as x[itex]\rightarrow[/itex]a

then we have lim g(x) = L as x[itex]\rightarrow[/itex]a

3. The attempt at a solution

I am having a hard time finding the right interval.

I am tempted to write:

f, g and h defined over (-∞,+∞)

Let ε>0, [itex]\exists[/itex] δ_{1}, δ_{2}>0:

f(x)[itex]\leq[/itex]g(x)[itex]\leq[/itex]h(x)

if lim f(x) = lim h(x) = L as x[itex]\rightarrow[/itex]-∞

then we have lim g(x) = L as x[itex]\rightarrow[/itex]-∞

but then if I follow the proof my prof gave me, I'd end up with

[itex]\forall[/itex]x 0<|x- -∞|<δ_{1}

and 0<|x- -∞|<δ_{2}

Thanks in advance

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# Proving the Squeeze when x->-infinity

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