Final answer:
The limit of the sequence x₍ = 3n³+2n−1/n³-n+2 is found by dividing the leading coefficients, which results in the limit being 3 as n approaches infinity.
Step-by-step explanation:
To find the limit of the sequence x₍ = 3n³+2n−1/n³-n+2 as n approaches infinity, we look at the highest powers of n in the numerator and the denominator. Here, the highest power is n³ in both. So, the limit can be found by dividing the coefficients of the highest power terms in the numerator and the denominator.
The leading term in the numerator is 3n³ and the leading term in the denominator is n³. Therefore, the limit of the sequence x₍ as n approaches infinity is the coefficient of n³ in the numerator divided by the coefficient of n³ in the denominator, which is 3/1 or simply 3.