Question

Find the limit

Answer 1

\[\large\lim_{x \rightarrow \infty}xe^{1-x}\]

Answer 2

So I changed it into \[\large\lim_{x \rightarrow \infty}\ \frac{ e^{1-x} }{ \frac{ 1 }{ x} }\]

Answer 3

Now, I applied the l'hopital's rule, but I think I get endless l'hopital's rule.

Answer 4

made it hard for yourself. try:


\(\large e \lim\limits_{x \rightarrow \infty} \dfrac{x}{e^{x}}\)

Answer 5

incidentally Steve, i think it would be fine actually to stop there as we know the exponential out grows the numerator, ie no need to process the L'Hôpital part of things

Answer 6

Ohh, I see, thank you Irishboy.