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Calculati :


lim x² sin[tex] \frac{1}{ x^{2} } [/tex] =?
x→∞


Răspuns :

[tex] \lim_{x \to \infty} x^{2} sin \frac{1}{ x^{2} } = \lim_{x \to \infty} \frac{sin \frac{1}{ x^{2} } }{ \frac{1}{ x^{2} } } =1 [/tex], se ajunge la nedeterminare  0/0, limita remacabila [tex] \lim_{u \to 0} \frac{sinu}{u}=1 [/tex]