Question

Image attached:

Answer 1

how do you change the indeterminate form of 0 times infinity?

Answer 2

the incredible nature of "0" (zero) is to make infinite "0" when you multiply them.
\(0\times\infty=0\)

Answer 3

or you can rewrite it as
\[\Large L=\lim_{x\to-\infty}\frac{x}{e^{x-2}}\]

Answer 4

\[e^{-2+x} x= e^{-2}e^x x=e^{-2}\frac{x}{e^{-x}}\]

Answer 5

it would be 2-x not x-2 @electrokid

Answer 6

lol yeah

Answer 7

but the information has been conveyed.

Answer 8

thanks for the idea. :)

Answer 9

limit then becomes infinity over infinity, and thus satisfies lhopital requirement