Calculus Examples

$lim_{x \to 0} x^{2} e^{\cos (\frac{1}{x})}$

Step 1

Since $x^{2} e^{- 1} \leq x^{2} e^{\cos (\frac{1}{x})} \leq x^{2} e^{1}$ and $lim_{x \to 0} x^{2} e^{- 1} = lim_{x \to 0} x^{2} e^{1} = 0$ , apply the squeeze theorem.

$0$