Question

lim (-3x+1)/sqrt(x^2+x) as x approaches -infinity

Answer 1

eyeball it

Answer 2

ignore everything but the leading terms
\[\frac{-3x}{\sqrt{x^2}}=\frac{-3x}{|x|}\] as \(x \) goes to \(-\infty\) you get 3

Answer 3

why do you ignore the other stuff?

Answer 4

because is \(x\to \infty\) they are irrelevant

Answer 5

think for example of
\[\lim_{x\to \infty}\frac{2x^2+x+7}{x^2+5x}\] if say
\[x=1000\] which is not a particularly large number, you have, in the numerator, a 2 in the millions place, some other stuff,
in the denominator you have a 1 in the millions place, and some other stuff
ratio is essentially 2 , the other stuff is in much lower places

Answer 6

Okay, thank you!