Se sostituissi l’infinito all’interno della parentesi.
1/x tende a 0.
log x tende a più infinito.
quindi avresti la somma di 0, 1 e più infinito…
A quel punto, si approssima ed è inutile considerare tutta la parentesi ma solo il fattore che risulta valere infinito.
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![\[\lim_{x \to +\infty} (1-x+xlnx)=\]](http://www.matebook.it/wp-content/ql-cache/quicklatex.com-a5ad2cdb3e0b112cd715e601f8a2b297_l3.png "Rendered by QuickLaTeX.com")
![\[\lim_{x \to +\infty} x(\frac 1x- 1+lnx) \simeq\]](http://www.matebook.it/wp-content/ql-cache/quicklatex.com-2f7b0f319918694b1b35fbb7effd0234_l3.png "Rendered by QuickLaTeX.com")
![\[\lim_{x \to +\infty} xlnx =+\infty\]](http://www.matebook.it/wp-content/ql-cache/quicklatex.com-f518a080567ec1113a84bd6cab8b9d8b_l3.png "Rendered by QuickLaTeX.com")
Potrebbe spiegarmi il passaggio dopo il segno di approssimazione.
Grazie
Se sostituissi l’infinito all’interno della parentesi.
1/x tende a 0.
log x tende a più infinito.
quindi avresti la somma di 0, 1 e più infinito…
A quel punto, si approssima ed è inutile considerare tutta la parentesi ma solo il fattore che risulta valere infinito.