[tex]\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} }) } )\\[/tex]
[tex]\frac{\lim_{x \to \infty} (x^{2} tan(\frac{1}{x^{2} } ))}{{\lim_{x \to \infty} cos(\frac{1}{x^{2} }) }}}[/tex]
[tex]\lim_{x \to \infty}(x^{2} sin(\frac{1}{x^{2} }))=1\\\\ \lim_{x \to \infty}cos(\frac{1}{x^{2}}))=1\\[/tex]
[tex]=\frac{1}{1\\}\\=1[/tex]
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[tex]\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} }) } )\\[/tex]
[tex]\frac{\lim_{x \to \infty} (x^{2} tan(\frac{1}{x^{2} } ))}{{\lim_{x \to \infty} cos(\frac{1}{x^{2} }) }}}[/tex]
[tex]\lim_{x \to \infty}(x^{2} sin(\frac{1}{x^{2} }))=1\\\\ \lim_{x \to \infty}cos(\frac{1}{x^{2}}))=1\\[/tex]
[tex]=\frac{1}{1\\}\\=1[/tex]