Question

Ex atașat in poza alăturată. 100 puncte.​

Answer 1

$\lim_{x \to \infty} (x^{2} tan(\frac{1}{x^{2} } ))\\\\ \lim_{x \to \infty} (\frac{(x^{2} sin\frac{1}{x^{2} } )}{cos(\frac{1}{x^{2} }) } )$

$\frac{\lim_{x \to \infty} (x^{2} tan(\frac{1}{x^{2} } ))}{{\lim_{x \to \infty} cos(\frac{1}{x^{2} }) }}}$

$\lim_{x \to \infty}(x^{2} sin(\frac{1}{x^{2} }))=1\\\\ \lim_{x \to \infty}cos(\frac{1}{x^{2}}))=1$

$=\frac{1}{1\\}\\=1$