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Find a value of constant k so a limit to infinity exists 
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#1
Sep3008, 10:19 PM

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1. The problem statement, all variables and given/known data
Find a value of the constant k such that the limit exists. 2. Relevant equations lim x to infinity of x^36/x^k+3 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. 


#2
Sep3008, 10:32 PM

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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
Oct108, 03:38 PM

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So would k be 3? I'm not sure I'm understanding..



#4
Oct108, 03:42 PM

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Find a value of constant k so a limit to infinity exists
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
Oct108, 03:46 PM

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oh my goodness. i just understood it now..thank you *bangs head on desk* :)



#6
Oct108, 04:42 PM

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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
Oct108, 04:48 PM

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and for k=3 the value of the limit would be 1, correct?



#8
Oct108, 05:14 PM

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