Question

How would you find the limits needed for this squeeze theorem question?

Answer 1

\[\frac{ Lim }{ x -> 0^{+} } \sqrt{e ^{x} - 1} * \cos(\frac{ \Pi }{ X^2 }) \]

Answer 2

Use the fact that \(|\cos x|\le1\). This means that for \(x>0\) (since you're approaching from the right),
\[\left|\sqrt{e^x-1}\cos\frac{\pi}{x^2}\right|\le\sqrt{e^x-1}\]

Answer 3

Oh okay, so since e^0 -1 = 0 and it can't be lower than 0 then it has to =0?