Christos
  • Christos
Solve the limit limit(x-->+infinity) sqrt((x-3)/x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
the square root grows slower so the limit will be zero
agent0smith
  • agent0smith
Divide both numerator and denominator by x, to solve it algebraically.
Christos
  • Christos
I am sorry the actual epression is sort(x-3/x)

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Christos
  • Christos
sqrt((x-3)/x)
anonymous
  • anonymous
\[\lim_{x\to \infty}\sqrt{\frac{x-3}{x}}\]?
Christos
  • Christos
Yes thats correct
anonymous
  • anonymous
then it is one since \(x-3\) and \(x\) grow at the same rate
anonymous
  • anonymous
think what it would be like if \(x\) was \(1,000\) you would have \[\sqrt{.993}\]
agent0smith
  • agent0smith
\[\Large \lim_{x\to \infty}\sqrt{\frac{x-3}{x}} = \sqrt {\lim_{x\to \infty}\frac{x-3} {x}}\]
Christos
  • Christos
bro I am trying to solve this limit actually http://screencast.com/t/Yoo5IO0bRPjD And I ended up in the expression above, but what you give me isnt the final answer, something must be wrong :(
agent0smith
  • agent0smith
@Christos that's a completely different expression... break it up using limit laws.
Christos
  • Christos
@satellite73
Christos
  • Christos
ohh let me try hold on
Christos
  • Christos
What do you mean by limit laws?
agent0smith
  • agent0smith
\[\Large = \lim_{x \rightarrow \infty} \sqrt{x^2 - 3x} -\lim_{x \rightarrow \infty} x\]
agent0smith
  • agent0smith
http://www.math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/SandS/lHopital/limit_laws.html
Christos
  • Christos
so thats infinity - infinity - infinity = +infinity?
agent0smith
  • agent0smith
From a graph it looks like it'll be -1.5, I'm just trying to find a way to show that algebraically.
Christos
  • Christos
It's ok man dont brother I found it thank you
agent0smith
  • agent0smith
Yeah i'm glad i didn't try to do it myself... wolfram gives a looooong solution: http://www3.wolframalpha.com/Calculate/MSP/MSP35891gdgbb0f2cc1ecie00005387i303c364idgg?MSPStoreType=image/png&s=42&w=433&h=1816

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