My teacher wanted us to resolve this limit using L'Hospital.
$\lim_{x\to +∞} \frac{(e^x)(x-1)}{x^2}$
But I can't understand why she derived the numerator, as it's an indefinite form (inf * inf) and I don't understand why L'Hospital's rule can be directly applied. Thank you in advance
Best Answer
If you expand the numerator as $xe^x-e^x$, then the expression at the limit is of the form $\infty/\infty$ and L'hopital's rule applies.