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anonymous
 4 years ago
\[\lim_{x \rightarrow 1}\frac{\int\limits_{1}^{x}\ln (3y3y ^{2}+y ^{3})dy}{(1x)^{3}}\]
anonymous
 4 years ago
\[\lim_{x \rightarrow 1}\frac{\int\limits_{1}^{x}\ln (3y3y ^{2}+y ^{3})dy}{(1x)^{3}}\]

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0l'hopital for this one

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0take derivative top and bottom get \[\lim_{x\rightarrow 1}\frac{x^33x^2+3x}{3(1x)^2}\]

ash2326
 4 years ago
Best ResponseYou've already chosen the best response.4start by differentiating numerator and denominator \[ \lim_{x>1} \frac{\frac{d}{dx}\int_{1}^{x} \ln(3yy^2+y^3) dy}{\frac{d}{dx} (1x)^3}\] we get \[ \lim_{x>1} \frac{ \ln(3xx^2+x^3)0}{3(1x)^2}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x\rightarrow 1}\frac{\ln(x^33x^2+3x)}{3(1x)^2}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i forgot the log, sorry

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Um the differentiation of the numerator is valid due to FTC 2 right?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yup. derivative of integral is integrand

ash2326
 4 years ago
Best ResponseYou've already chosen the best response.4now on differentiating again \[ \lim_{x>1} \frac{\frac{3x^26x+3}{x^33x^2+3x}}{6(1x)}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0gonna hae to do it again though

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@ash x\rightarrow 1 \[x\rightarrow 1\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0sat: x \to 1 also work ;)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0jeez and all this time. pluse i spell "rightarrow" wrong half the time

ash2326
 4 years ago
Best ResponseYou've already chosen the best response.4Let's differentiate it for the last time \[\lim_{x\rightarrow1} \frac{\frac{(6x6)(x^33x^2+3x)(3x^26x+3)(3x^26x+3)}{(x^33x^2+3x)^2}}{+6}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0haha I was there too :P

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i will post this in latexpractice

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Sat, have you seen this http://openstudy.com/users/foolformath#/updates/4f2d5be5e4b0571e9cba67c0

ash2326
 4 years ago
Best ResponseYou've already chosen the best response.4If we substitute x=1 , numerator is zero and denominator is finite so the answer is 0
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