Help finding limit of n to infinity of these 3 problems?

1. lim (n --> infinity) (n^3 - 10) / (3n + 1)

----- think of n as money --- and do some rounding
look at the denominator --- if n is $1,000,000,000 the 3n+ 1 is 3,000,000,000 + 1 <<< who cares about the 1??? so round to 3,000,000,000 or 3n
--- same for the numerator --- n^3 -10 --- (1,000,000,000)^3 - 10 = 1,000,000,000,000,000,000,000,000 - 10 <<< who cares about the 10???
so n^3 -10 rounds to n^3 for really large numbers

so --- lim (n --> infinity) (n^3 - 10) / (3n + 1) becomes
= lim (n --> infinity) (n^3) / (3n) ---- now cancel
= lim (n --> infinity) (n^2) / (3)
---- large numbers squared just get larger --- dividing by 3 can be ignored

final answer --- limit = infinity

2. answer --- 5 ... see if you can figure out why
3. answer --- infinity

2. (5n^4+3)/n^4 = 5 + (3/n^4)
as n → ∞ (3/n^4) → 0
so as n → ∞ lim 5n^4 + 3 / n^4 = 5

1 and 3 answer is infinity.. since as n → ∞ any positive power of n → ∞