Question

please help :( evaluate lim x->positive infinity 2x-1/x-1

Answer 1

well, for one \(x \ne 0 because that'd make the denominator 0 and thus the fraction undefined

any value > 1 onwards, will yield a value in the denominator of "x-1" and a value on the numerator of "2x-1", or x + x -1
so notice "2x-1" will yield a bigger number
than "x-1"

which means the numerator will always be bigger than the denominator by "x"
so if the denominator says turns out to be 25, the numerator will be x +25

Answer 2

so, where's that number going to? what's its limit?
well, you have a rational expression, and the limit will occurr at an asymptote
as "x" is moving fast rightwards, "y" is moving upwards, so that means a horizontal asymptote

so, in this case the numerator and denominator are of the same degree, thus the horiziontal asymptote will occurr at the leading coefficient atop/bottom

Answer 3

well, for one \(x \ne 0\) because that'd make the denominator 0 and thus the fraction undefined

Answer 4

ack I meant \(x \ne 1\)

Answer 5

1 btw is the vertical asymptote

Answer 6

\[\lim_{x \rightarrow \infty } 2x-1/x-1\]

Answer 7

yes

Answer 8

i'm sorry, i dont understand. your explanation is a little too complicated for me

Answer 9

have you done asymptotes yet?

Answer 10

not yet

Answer 11

ok, well, then you can just make a few values for "x" and see where "y" is heading to
keep in mind that 2x -1 ==> x + x -1, and that will always be more than x-1 by x so
if x = 5
and onwards

$$
\begin{matrix}
x && y\\
5 & &\cfrac{5-4}{4}\\
\hline
10 & &\cfrac{10-9}{9}\\
\hline
25 & &\cfrac{25-24}{24}
\end{matrix}
\\
$$

Answer 12

did I get that...

Answer 13

haemm, no :/

Answer 14

let's see, 2x -1 = x +( x -1) so, the numerator will be bigger by more

Answer 15

$$
\begin{matrix}
x && y\\
\color{red}{5} & &\cfrac{\color{red}{5}+4}{4}\\
\hline
\color{red}{10} & &\cfrac{\color{red}{10}+9}{9}\\
\hline
\color{red}{25} & &\cfrac{\color{red}{25}+24}{24}
\end{matrix}
\\
$$

Answer 16

so, the 1st "y" up there will be
9/4 and then
19/9 and then
49/24
...
and so on
notice where or how close it's moving towards

Answer 17

5/4 = 1.25
19/9 = 2.11
49/24 = 2.04

if say I use 1,000,000
so I'd get

1000000-1 = 999999

thus

1999999/999999 = 2.000001

Answer 18

thank you :)

Answer 19

yw