Teorema del Sándwich
∞ Límite 1
$$ \lim_{x ~ \to ~ 0} ~ x \sin{\left(\frac{1}{x}\right)} ~~~~ , ~~~~ \lim_{x ~ \to ~ 0} ~ x \cos{\left(\frac{1}{x}\right)}$$
∞ Límite 2
$$ \lim_{x ~ \to ~ 0} ~ x^2 \sin{\left(\frac{1}{x}\right)} ~~~~ , ~~~~ \lim_{x ~ \to ~ 0} ~ x^2 \cos{\left(\frac{1}{x}\right)}$$
∞ Límite 3
$$ \lim_{x ~ \to ~ 0} ~ x^4 \sin{\left(\frac{2}{x}\right)} ~~~~ , ~~~~ \lim_{x ~ \to ~ 0} ~ x^4 \cos{\left(\frac{2}{x}\right)}$$
∞ Límite 4
$$ \lim_{x ~ \to ~ 0^+} ~ \sqrt{x} \sin^2{\left({\frac{\pi}{x}}\right)} ~~~~ , ~~~~ \lim_{x ~ \to ~ 0^+} ~ \sqrt{x} \cos^2{\left({\frac{\pi}{x}}\right)}$$
∞ Límite 5
$$ \lim_{x ~ \to ~ 0^+} ~ \sqrt{x} e^{\sin{\left({\frac{\pi}{x}}\right)}} ~~~~ , ~~~~ \lim_{x ~ \to ~ 0^+} ~ \sqrt{x} e^{\cos{\left({\frac{\pi}{x}}\right)}}$$
∞ Límite 3
$$ \lim_{x ~ \to ~ 0} ~ x^4 \sin{\left(\frac{2}{x}\right)} ~~~~ , ~~~~ \lim_{x ~ \to ~ 0} ~ x^4 \cos{\left(\frac{2}{x}\right)}$$
∞ Límite 4
$$ \lim_{x ~ \to ~ 0^+} ~ \sqrt{x} \sin^2{\left({\frac{\pi}{x}}\right)} ~~~~ , ~~~~ \lim_{x ~ \to ~ 0^+} ~ \sqrt{x} \cos^2{\left({\frac{\pi}{x}}\right)}$$
∞ Límite 5
$$ \lim_{x ~ \to ~ 0^+} ~ \sqrt{x} e^{\sin{\left({\frac{\pi}{x}}\right)}} ~~~~ , ~~~~ \lim_{x ~ \to ~ 0^+} ~ \sqrt{x} e^{\cos{\left({\frac{\pi}{x}}\right)}}$$
∞ Límite 5
$$ \lim_{x ~ \to ~ 0^+} ~ \sqrt{x} e^{\sin{\left({\frac{\pi}{x}}\right)}} ~~~~ , ~~~~ \lim_{x ~ \to ~ 0^+} ~ \sqrt{x} e^{\cos{\left({\frac{\pi}{x}}\right)}}$$
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