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Calculus/Squeeze Theorem

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Expert: - 10/22/2011


Question
Squeeze Theorem May2010
Squeeze Theorem May201  
Hi Prof,

I am busy preparing for my Calculus examination by working through previous question papers. I have attached image of question as it is easier to write it.I want you to check if I did the part where I need to proof squeeze Theorem correctly and in the second part of the same question I need to apply it.This is where I am not sure what I need to do.

Can you please advise me.Thanks again.

Answer
1. The only problem on the 1st question is in the line -1 < sin(1/h) < 1,
it should really read -1 < sin(1/h) / h < 1, but the other than that,
the problem is done correctly.

2. We known that 0 < f(x) < x² since sin(x) is positive when x is close to 0 on the positive side, and sin(x) < 1.  Since the lim(x->0)0 = 0 and lim(x->0)x² = 0, then the lim(x->0) f(x) = 0.

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