Limit Problem

  • Thread starter icosane
  • Start date
  • #1
48
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Homework Statement



Lim as x goes to infinity of sqrt(x^2 + 1) / x


The Attempt at a Solution



know you are supposed to divide by the highest power of x, but how does that work when you have an x^2 within a sqrt?
 

Answers and Replies

  • #2
danago
Gold Member
1,122
4
Try writing x2+1 as x2(1+1/x2).

See if that helps.
 
  • #3
HallsofIvy
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And remember that [itex](1/x)\sqrt{x^2+ 1}= \sqrt{(1/x^2)(x^2+ 1}[/itex]
 
  • #4
76
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put your x in to the square root by making it X^2....then it will be easy because you will get something like
limit x--->infinity sqrt(1+1/X^2)
and when x goes to infinity 1/X^2 goes to zero
so your final limit will go to 1
hope you got it!!!!!!!!!!!!
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
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963
You've got three responses saying the same thing in different ways!
 

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