Question

Show that \[\lim_{x \rightarrow 0^{+}}(1/x - 1/x ^{2}) = -\infty\]

Answer 1

An idea...
I think u get infinit-infinit= undefined form so u must use L'Hopital's rule....

Answer 2

yes inf-inf=inf. but how -inf?

Answer 3

no inf-inf is undefined

Answer 4

I know. madam but in question it must be -inf.

Answer 5

hey. anyone help me with this?

Answer 6

subtract

Answer 7

@satellite73 help me please

Answer 8

yeah. but how to get -inf?

Answer 9

\[\frac{1}{x}-\frac{1}{x^2}=\frac{x-1}{x^2}\] now take the limit

Answer 10

it will go to infinity.

Answer 11

x is going to zero, so denominator is going to zero and numerator is going to -1
denominator is always positive so you go to minus infinity

Answer 12

but one thing. if I take lim at this step i.e.
1/x - 1/x^2
Then?

Answer 13

you cannot take the limit in that step by taking the limits separately
you have to subtract first
if you try to take the limit one piece at the time you get \(\infty-\infty\) which is undetermined

Answer 14

oh .. that's fine thanx buddy.

Answer 15

but according to howard anton calculus we can take limit separately Theorem#2.2.2 6th edition a new horizon.

Answer 16

@satellite73

Answer 17

http://www.wolframalpha.com/input/?i=plot+y+%3D+1%2Fx+-+1%2Fx%5E2+from+0+to+1