sarraelghoul62
Answered

Find the limit of (lnx)³/x as x approaches infinity.

Now when I take an arbitrary very big number and try calculating the limit with a calculator, it gives 0.

On the other hand I thought about this:

g(x)=x³

lim(x goes to + inf) g(x)=+inf

lim(x goes to +inf) g(x)/x = +inf

lim(x goes to +inf) lnx=+inf

then

lim(x goes to +inf) g(lnx)/x=+inf

which is obviously wrong.Help????

Verified Answer :

apologiabiology

ok, so one way is like your way

so
if we test some numbers
for x=10
we get about 12.3/10≈1.2
for x=100000
we get 1522.03/100000≈0.01522
the top number keeps getting smaller reletive to bottom number
when x=1000000000
we get 8899.68/1000000000≈0.000009

we notice the bottom number is increaseing at a faster rate that the botom one
when x approaches infinity,the bottom number will be so big it will become a fraction that evaluates to basically zero becuase it evaluates to a very small number that is negligible

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