anonymous
  • anonymous
What is the limit of (x)÷((1/1+x)−1) as x approaches 0?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\large \lim_{x \rightarrow 0} \frac{ x }{ \left( \frac{ 1 }{ 1+x }-1 \right) }\] this?
anonymous
  • anonymous
yes!
anonymous
  • anonymous
Lets start off by simplifying the denominator you can use the following \[\frac{ a }{ b } \pm \frac{ c }{ d } \implies \frac{ ad \pm bc }{ bd }\]

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anonymous
  • anonymous
Go ahead and see what you get
anonymous
  • anonymous
So then would the denominator be \[(1-1+x)/(1+x)\]
anonymous
  • anonymous
wait, the first part should be 1-1-x I think.
anonymous
  • anonymous
\[\huge \lim_{x \rightarrow 0} \frac{ x }{ \left( \frac{ 1-1(1+x) }{ 1+x } \right) } = \lim_{x \rightarrow 0}\frac{ x }{ \left( \frac{ 1-1-x }{ 1+x } \right) }\] correct?
anonymous
  • anonymous
Keep simplifying :)
anonymous
  • anonymous
Yeah. And then I just use the reciprocal of the denominator and plug in the 0, and I get -1?
anonymous
  • anonymous
Bingo!
anonymous
  • anonymous
thank you!!
anonymous
  • anonymous
Yw :)

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