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

by madgab89
Tags: constant, exists, infinity, limit
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 P: 22 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^3-6/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.
 Sci Advisor HW Helper Thanks P: 25,235 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.
 P: 22 So would k be 3? I'm not sure I'm understanding..
 Sci Advisor HW Helper Thanks P: 25,235 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.
 P: 22 oh my goodness. i just understood it now..thank you *bangs head on desk* :)
 P: 22 so to show that say for k=4 the limit is 0, would I just divided each term top and bottom by x^4?
 P: 22 and for k=3 the value of the limit would be 1, correct?
Sci Advisor
HW Helper
Thanks
P: 25,235
 Quote by madgab89 and for k=3 the value of the limit would be 1, correct?
Right on both counts.

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