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The nth term of a sequence is represented by ((2n^5)+(25n^2)+(32n)-(15))/((6n^4)+(2n^3)-(11n^2)-2n+17)

What is the limit of the nth term as x becomes increasingly large? 

Options: 0,1/3,3, or the limit doesn’t exist.

 

I think the limit doesn’t exist but i don’t know!! Please help if possible

 Jun 2, 2021
 #1
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2n^5  +25n^2 + 32n - 15

________________________

6n^4 + 2n^3  -11n^2-2n+ 17

 

You are correct.....the limit does not exist

 

If  we  divide  every term by  n^4   and then  let  n  approach infinity.....we will be  left with

 

2n  + 0 + 0   +  0

________________  =     (2/6)n    =     n / 3     =  inf  / 3   =    the limit does not exist

  6  + 0 + 0 + 0 + 0

 

This will alwas happen  when  we  have  a higher power polynomial /  a lower power polynomial

 

cool cool cool

 Jun 2, 2021

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