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anonymous
 one year ago
Just a small question...
anonymous
 one year ago
Just a small question...

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Having something like this... \[\lim _{x \rightarrow0}e ^{(\frac{ 3 }{ x })\ln(13x)}\] is it possible to bring the e out and get this... \[e \lim _{x \rightarrow0}(\frac{ 3 }{ x })\ln (13x)\]

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5\(\large\color{black}{ \displaystyle \lim_{x\rightarrow 0}e^{\frac{3}{x}\ln(13x)} }\) \(\large\color{black}{ \displaystyle e^{\lim_{x\rightarrow 0}\frac{3}{x}\ln(13x)} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5is this better ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh yes! That's it! But what's the logic behind this step? I don't exactly understand

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5you should review the limit properties

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5I mean, nothing offensive, but find a link and read them over. you can find them absolutely everywhere

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No worries at all! Thanks for the help!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5\(\LARGE\color{black}{ \displaystyle e^{\lim_{x\rightarrow 0}\frac{3\ln(13x)}{x}} }\) \(\LARGE\color{black}{ \displaystyle e^{\lim_{x\rightarrow 0}\frac{3\ln(13x)}{x}} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5did this step just now make sense?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5now both top and bottom go to infinity

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5go ahead and apply L'H's

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is that the same as what you wrote before? (e^ lim....)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5I didn't change the value. I didn't do any unallowed step

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5am I allowed to multiply times 1 twice? (on the bottom and in front of the lim)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5\(\LARGE\color{black}{ \displaystyle e^{\lim_{x\rightarrow 0}\frac{3\ln(13x)}{x}} }\) \(\LARGE\color{black}{ \displaystyle e^{\lim_{x\rightarrow 0}\frac{3\ln(13x)}{x}} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5now apply the lhs to the limit. questions about how I got till there?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would we have to multiply by 1 ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5what do you mean? where?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5I already got it to approach oo

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5to approach oo on top and bottom

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohhh but it should be approaching 0

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5ln(10)=1 x=0=0

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5why am I saying oo ? apologize

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5\(\LARGE\color{black}{ \displaystyle e^{\lim_{x\rightarrow 0}\frac{3\ln(13x)}{x}} }\) top and bottom DO go to 0. ln(1)=0 and (0)=0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So it's just the first line right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I mean I don't get why we'd have a lim and x in the denominator

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5\(\LARGE\color{black}{ \displaystyle e^{\lim_{x\rightarrow 0}\frac{3\ln(13x)}{x}} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5it was my mistake, i was thinking of infinity b/c i thought the lim > (oo)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5but in can x>0 take LHS as it is

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5\(\LARGE\color{black}{ \displaystyle e^{\lim_{x\rightarrow 0}\frac{3\ln(13x)}{x}} }\) \(\huge \color{black}{ \displaystyle e^{\lim_{x\rightarrow 0}\frac{3\frac{3}{13x}}{1}} }\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh okie dokie! So now its just L'Hopital right?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5yes... that i did d/dx on top and bottm

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5\(\huge \color{black}{ \displaystyle e^{\lim_{x\rightarrow 0}\frac{9}{13x}} }\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I get 9 on the top but on the bottom isn't the derivative of x just 1?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5yes, 3 replies ago i did the derivative

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohh cause its a fraction over a fraction!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5wel, 1 on bottom for x, and the derivative of ln(13x) is a fraction 3/(13x)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5ok, what is your answer?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is it e^9 ? So 1/e^9

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5yes, there you go!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5I can review the limit properties with you if you want...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Finally! Haha! Thanks so much! I've been bugging you a lot today! Im so sorry!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5Ok, you welcome. You can choose to rvw limit properties later alone, or if you would like to, I can type more here...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's fine! I can look it up on Google real quick! :D

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.5Alright. Enjoy:) ... not a problem.
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