Question

limit with x approaching infinity at (2x -1)/(|x| - 3)

Answer 1

l'hopital's rule

Answer 2

can you show me with and without hopitals plz

Answer 3

I don't think that's necessary, though you can certainly do that.

\(|x|=x\) for positive \(x\), which is the case since \(x\to\infty\).

Answer 4

yeahbut i still dont get it

Answer 5

\[\lim_{x\to\infty}\frac{2x-1}{|x|+3}=\lim_{x\to\infty}\frac{2x-1}{x+3}=\lim_{x\to\infty}\frac{2-\frac{1}{x}}{1+\frac{3}{x}}=\cdots\]

Answer 6

2?

Answer 7

Sorry, minus in the denominator, not plus. The answer doesn't change anyway.

Answer 8

yes

Answer 9

thank you