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anonymous
 3 years ago
Find the Limit:
anonymous
 3 years ago
Find the Limit:

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0take the log take the limit exponentiate

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I am allowed to use L'Hospital's rule. I am not sure how I would use it though...

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Yep... I am not sure how that would help though...

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Hmm Okay... Let's see...

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0probably easier if you write \[\frac{\ln(5x3)\ln(5x+7)}{\frac{1}{3x+1}}\]

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow \infty} \frac{ \frac{ 5 }{ 5x3 }\frac{ 5 }{ 5x+7 } }{ \frac{ 3 }{ (3x+1)^2 } }\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ugly retricealgebra from here on in have fun, but you will get a rational expression so limit is same as horizontal asymptote

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0actually it is not that bad

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Yep. I think I see why.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\frac{(3x+1)^2}{3}\times \frac{50}{(5x3)(5x+7)}\] and not need to multiply out, just look at the ratio of the leading coefficients

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i 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 \(6\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and don't forget to exponentiate at the end

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So I got 1/e^6 or e^6.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0:) . Thanks a million :) .
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