Question

Need help with a limit

Answer 1

\[\lim_{t \rightarrow \infty} \frac{ t-t \sqrt{t} }{ 2\sqrt{t ^{3}}+3t-5 } \]

Answer 2

nice one. give me a minute

Answer 3

is \[2\sqrt{t^{3}}=2t?\]

Answer 4

nope nvm

Answer 5

its
\[2t\sqrt{t}\]

Answer 6

try dividing nr and dr by that^

Answer 7

Have you considered dividing each term by \(t^{3/2}\)?

Answer 8

yea, im trying that

Answer 9

Better yet, just observe that the "degree" of the denominator is the same as the "degree" of the numerator and immediately call out in an excited voice that the limit is -1/2!! That's how it worked back in your Rational Function days.

Answer 10

oh wait lol totally went over my head that \[t \sqrt{t}=t ^{\frac{ 3 }{ 2 }}\]

Answer 11

yeah, that makes sense. i agree -1/2

Answer 12

that makes a lot easier now Thanks guys

Answer 13

yup I got -1/2