Question

Limis as x approaches negative infinity of :
x/e^x= - infinity
why ?

Answer 1

because the limit \(x\to -\infty\) of \(e^x\) is \(0\) through positive numbers

Answer 2

but then we get x/0

Answer 3

\(\frac{x}{0}\) is not a number

Answer 4

oh i get it

Answer 5

\(e^x\) gets smaller and smaller, by which i mean it gets closer and closer to zero, but of course is never actually equal to zero
imagine it was \(0.001\)
\(x\) is going to \(-\infty\) and so imagine it is \(-10000\)

Answer 6

we get -infinity/1

Answer 7

no, not one in the denominator, a very very small positive number in the denomiator

Answer 8

yeah looking at the graph makes it more clear thanks

Answer 9

trying it with say \(x=-100\) would give you a good idea too, and \(-100\) is a small step on the way to \(-\infty\)

Answer 10

right not one but a positive small number great