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anonymous
 4 years ago
Find the limit:
anonymous
 4 years ago
Find the limit:

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[(\int\limits_{0}^{x}(3t1)^{10} dt)/3x\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0as x approaches 0 I'm confused because the question has two variables: x and t. How should I approach this?

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.1Evaluate the limit in the top first.

watchmath
 4 years ago
Best ResponseYou've already chosen the best response.1sorry, I didn't see 3x :)

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.1Oh right. L'Hopital's rule is the best choice: \[\frac{d}{dx}\int\limits_0^x(3t1)^{10}dt=(3x1)^{10}.\]

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.1The derivative of the bottom is obviously 3. Hence the limit is \(\frac{3(0)1)^{10}}{3}=\frac{1}{3}\).

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0This makes sense, but how did you know to use l'hopital's rule?

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.1If we plug x=0, you will get \(\frac{0}{0}\). If you plug x in the top, you get an integral from 0 to 0, which results in a value of 0. I think it's very obvious in the denominator.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh okay, thanks a ton!
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