Shayaan_Mustafa
  • Shayaan_Mustafa
Show that \[\lim_{x \rightarrow 0^{+}}(1/x - 1/x ^{2}) = -\infty\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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angela210793
  • angela210793
An idea... I think u get infinit-infinit= undefined form so u must use L'Hopital's rule....
Shayaan_Mustafa
  • Shayaan_Mustafa
yes inf-inf=inf. but how -inf?
angela210793
  • angela210793
no inf-inf is undefined

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Shayaan_Mustafa
  • Shayaan_Mustafa
I know. madam but in question it must be -inf.
Shayaan_Mustafa
  • Shayaan_Mustafa
hey. anyone help me with this?
anonymous
  • anonymous
subtract
Shayaan_Mustafa
  • Shayaan_Mustafa
@satellite73 help me please
Shayaan_Mustafa
  • Shayaan_Mustafa
yeah. but how to get -inf?
anonymous
  • anonymous
\[\frac{1}{x}-\frac{1}{x^2}=\frac{x-1}{x^2}\] now take the limit
Shayaan_Mustafa
  • Shayaan_Mustafa
it will go to infinity.
anonymous
  • anonymous
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
Shayaan_Mustafa
  • Shayaan_Mustafa
but one thing. if I take lim at this step i.e. 1/x - 1/x^2 Then?
anonymous
  • anonymous
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
Shayaan_Mustafa
  • Shayaan_Mustafa
oh .. that's fine thanx buddy.
Shayaan_Mustafa
  • Shayaan_Mustafa
but according to howard anton calculus we can take limit separately Theorem#2.2.2 6th edition a new horizon.
Shayaan_Mustafa
  • Shayaan_Mustafa
@satellite73
experimentX
  • experimentX
http://www.wolframalpha.com/input/?i=plot+y+%3D+1%2Fx+-+1%2Fx%5E2+from+0+to+1

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