Question

The nth term of a sequence is represented by 2n^4+25n^2+32n−15

____________________

6n^4+2n^3−11n^2−2n+17.

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



A)0

B)1/3

C)3

D)The limit does not exist.

Answer 1

Post it like this ....
(2n^4+25n^2+32n−15)/(6n^4+2n^3−11n^2−2n+17)

You want:
limit (2n^4+25n^2+32n−15)/(6n^4+2n^3−11n^2−2n+17) , as n ---> ∞
divide each term by the highest power of n , that is , by n^4
= lim (2 + 25/n^2 + 32/n^3 − 15/n^4)/(6 + 2/n − 11/n^2 − 2/n^3 + 17/n^4) as n ---> ∞
as n ---> ∞, all terms that still have n's in them will approach zero, so
lim (2 + 25/n^2 + 32/n^3 − 15/n^4)/(6 + 2/n − 11/n^2 − 2/n^3 + 17/n^4) as n ---> ∞
= lim (2/6)
= 1/3

Answer 2

is the correct answerr

Answer 3

is this the right answer?