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

by madgab89
Tags: constant, exists, infinity, limit
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madgab89
#1
Sep30-08, 10:19 PM
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.
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Dick
#2
Sep30-08, 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.
madgab89
#3
Oct1-08, 03:38 PM
P: 22
So would k be 3? I'm not sure I'm understanding..

Dick
#4
Oct1-08, 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.
madgab89
#5
Oct1-08, 03:46 PM
P: 22
oh my goodness. i just understood it now..thank you *bangs head on desk* :)
madgab89
#6
Oct1-08, 04:42 PM
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?
madgab89
#7
Oct1-08, 04:48 PM
P: 22
and for k=3 the value of the limit would be 1, correct?
Dick
#8
Oct1-08, 05:14 PM
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Quote Quote by madgab89 View Post
and for k=3 the value of the limit would be 1, correct?
Right on both counts.


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