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Dido525Best ResponseYou've already chosen the best response.0
\[\lim_{x \rightarrow \infty}(\frac{ 5x3 }{ 5x+7 })^{3x+1}\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
take the log take the limit exponentiate
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
I am allowed to use L'Hospital's rule. I am not sure how I would use it though...
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
So I get it's (infinity/infinity)^(infinity) but I am not sure how to go from there...
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Yep... I am not sure how that would help though...
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
\[(3x+1)\ln(\frac{5x3}{5x+7})\] now you \(\infty\times 0\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
rewrite as \[\frac{\ln(\frac{5x3}{5x+7})}{\frac{1}{3x+1}}\] now you have \[\frac{0}{0}\] and now you can use l'hopital
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Hmm Okay... Let's see...
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
probably easier if you write \[\frac{\ln(5x3)\ln(5x+7)}{\frac{1}{3x+1}}\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
@satellite73 : Okay so I have: \[\lim_{x \rightarrow \infty} \frac{ \frac{ 5 }{ 5x3 }\frac{ 5 }{ 5x+7 } }{ \frac{ 2 }{ (3x+1)^2 } }\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
denominator is wrong
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
\[\lim_{x \rightarrow \infty} \frac{ \frac{ 5 }{ 5x3 }\frac{ 5 }{ 5x+7 } }{ \frac{ 3 }{ (3x+1)^2 } }\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
ugly retricealgebra from here on in have fun, but you will get a rational expression so limit is same as horizontal asymptote
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
actually it is not that bad
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Yep. I think I see why.
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
\[\frac{(3x+1)^2}{3}\times \frac{50}{(5x3)(5x+7)}\] and not need to multiply out, just look at the ratio of the leading coefficients
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
i mean you have to be a bit careful but the leading coefficient of the numerator is \(9\times 50\) and the leading coefficient of the denominator is \(3\times 25\) so you the ratio is \(6\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
and don't forget to exponentiate at the end
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
So I got 1/e^6 or e^6.
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
:) . Thanks a million :) .
 one year ago
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