Find a value of constant k so a limit to infinity exists

  • Thread starter madgab89
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  • #1
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Find a value of constant "k" so a limit to infinity exists

Homework Statement



Find a value of the constant k such that the limit exists.

Homework Equations



lim x to infinity of

x^3-6/x^k+3

The Attempt at a Solution


I started by setting the equation equal to infinity and attempted to rearrange it but got pretty much nowhere. I also broke it up using limit rules and also ended up nowhere.
 

Answers and Replies

  • #2
Dick
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Can you guess what a k might be? For the limit to exist the numerator and denominator have to grow at similar rates as x->infinity.
 
  • #3
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So would k be 3? I'm not sure I'm understanding..
 
  • #4
Dick
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Yes, k=3 is one value that works. What's the limit in that case? Can you show if k>3 the limit is 0 (so it exists) and if k<3 the limit is infinity (so it doesn't exist)? You were just asked to find 'a value'. There are lots of choices.
 
  • #5
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oh my goodness. i just understood it now..thank you *bangs head on desk* :)
 
  • #6
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so to show that say for k=4 the limit is 0, would I just divided each term top and bottom by x^4?
 
  • #7
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and for k=3 the value of the limit would be 1, correct?
 
  • #8
Dick
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and for k=3 the value of the limit would be 1, correct?

Right on both counts.
 

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