Squeeze Theorem: If x^3 ≤ f(x) ≤ x for x in [-1,1], find lim x→0 f(x)...

[jlxharville]

Squeeze Theorem: If x^3 ≤ f(x) ≤ x for x in [-1,1], find lim x→0 f(x)...

Hey everyone,

I'm struggling hard with squeeze theorem. Can someone please help me solve this problem? I get the idea behind how Squeeze theorem works as a function, but as soon as they added [-1, 1] I can't seem to find any problems like this one to reference.

If x^3 ≤ f(x) ≤ x for x in [-1,1], find lim x→0 f(x) if it exists. Hint: This is the Squeeze Theroem.

A) 0
B) does not exist
C) 1
D) -1

How do I go about solving this type of problem? Thank you!

 

[MarkFL]

According to the Squeeze Theorem, if you can say that:

\(\displaystyle \displaystyle \lim_{x\to0}x^3=\lim_{x\to0}x=L\)

then you may also say:

\(\displaystyle \displaystyle \lim_{x\to0}f(x)=L\)

 

[stapel]

I'm struggling hard with squeeze theorem. Can someone please help me solve this problem? I get the idea behind how Squeeze theorem works as a function, but as soon as they added [-1, 1] I can't seem to find any problems like this one to reference.

If x^3 ≤ f(x) ≤ x for x in [-1,1], find lim x→0 f(x) if it exists. Hint: This is the Squeeze Theroem.

How do I go about solving this type of problem?

How does having a specified interval (in this case, around the target value of zero) differ from what you've worked with previously? What is the precise statement (in your particular book) of the Squeeze Theorem?

Thank you!