Question

Evaluate the following limit, if it exists. Give exact value

lim (2-5/x + 7/x^2)
x->-infinity

Answer 1

\[\lim_{x \rightarrow -\infty} \left( 2-\left(\begin{matrix}5 \\ x\end{matrix}\right) + \frac{ 7 }{ x^{2} }\right)\]

Answer 2

2

Answer 3

proof please

Answer 4

Ok...could you tell me how you got that answer?

Answer 5

It is open secret I don't need to poof it.

Answer 6

Ok well thanks anyways. I'm just trying to understand how to do this question, not looking for just the answer

Answer 7

if you sub in -infinity for x, the last 2 terms are insignificant and can be ignored.

Answer 8

the deal is that as x->infty, 1/x->0
hence any finite number divided by \(\pm\infty\) is zero
so \[\lim_{x\to\infty}\frac5x=\frac5\infty=0\]and\[\lim_{x\to\infty}\frac7{x^2}=\frac7\infty=0\]so all that's left is the 2

Answer 9

same for negative infinity...

Answer 10

oh ok, thank u petewe. So if it was x->2 I would just substitute that number in for x?

Answer 11

yes.

Answer 12

oh wow, that's easy enough. Thank you both petewe and Turning Test!

Answer 13

happy to help :)