Question

find the limit x-->0 (x+1)/(x^2(x+7))

Answer 1

is that \(\large \lim_{x\to o}\frac{x+1}{x^2(x+7)}\)

Answer 2

@JonC

Answer 3

@JonC: What kind of a question is this? I don't get it!

Answer 4

yes

Answer 5

if so factor x^2 from top
so you get x^2(1/x +1/x^2) then cancel x^2
and evaluate the limit after

Answer 6

find the limit ?

Answer 7

Okay see what i said!

Answer 8

you need to factor x^2 from the top so you can cancel it

Answer 9

Do you get it?

Answer 10

no sorry

Answer 11

Oh hold a second my bad I'm thinking about x===>OO for the top lol

Answer 12

Ok forgot what i said lol
you need to do left and right limit

Answer 13

for the left and right limits
you just plugging zero and think about the left side of zero
or right side of zero

Answer 14

for the left one you should get 0+1/0(0+7) that x^2 will turn any small number near zero be positive so you get in the bottom 0+
so you got 1/0+ which is +OO

Answer 15

@xapproachesinfinity you're talking crap stop it

Answer 16

then you do the same thing with right side limit 0+
the first one was 0- and changed to 0+ because we are squaring x^2

Answer 17

that's not how you should talk! if this is not relevant then say it in a nice way
and offer a better way

Answer 18

Or...... you're just talking sense.

Answer 19

Fine you're talking "sense". There. Better now? You did a great job on the response though.

Answer 20

:)

Answer 21

sorry for acting mean to you @xapproachesinfinity you did good

Answer 22

here is the picture @JonC
first limit from the left
\(\large \lim_{x\to0^{-}}\frac{x+1}{x^2(x+7)}=\lim_{x\to0^-}\frac{0+1}{0^+(0+7)}\)

Answer 23

No worries ^^

Answer 24

so \(\large \lim_{x\to o-}\frac{1}{0^+}=\infty\)
you do the same with right side limit

Answer 25

like i said when you evaluate small number close to zero and negative
like for example -0.001
-0.001+7= gives a positive number
and (-0.001)^2=positive as well
so you get a number very close to zero but positive
that's why we right it as 1/0+

Answer 26

Hope that makes sense to you!
just something i want to throw here
1/0+=oo
think about powers of then in the bottom like this \(10^{-2}\) so surely \(1/10^{-2}=10^2\) the more you get close to zero the more 1/0 blows to infinity