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anonymous
 one year ago
I do not understand how to do this.
anonymous
 one year ago
I do not understand how to do this.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Write limn→∞∑k=1n(2+k∗(5/n))3∗5/n as a definite Integral

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1I can't understand the notation. \(\lim_{n\rightarrow \infty}ln(2+k(5/n))^{3}\cdot\dfrac{5}{n}\)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that is the notation

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Not quite. What is the "k=" doing in there?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im not sure thats what my problem says though. Think it stands for constant

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh im sorry let me rewrite equation real quick

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Maybe you can use the [Draw] feature?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\lim_{n \rightarrow \infty}\sum_{k=1}^{n}(2+k*5/n)^3 *5/n\]

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Well, that makes more sense!

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Did you just learn, in that moment, just enough LaTeX to write that? Good work.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you. Now i am unsure of how to convert that to a definite integral

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Let's remember the definition of a Riemann Integral. Roughly, you chop things up into smaller and smaller pieces and never stop doing this. This is EXACTLY the function of 'n' in the given expression. \(n \rightarrow \infty\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0still to not understand how to convert

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Try a couple values for n and see how it goes.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what to do you mean try n values?

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Do n=1, then do n = 2. Look for anything familiar or consistent.

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1The first thing I noticed was that \(5/n\) is constant for a given value of n. This suggests an equivalent expression: \(\lim_{n\rightarrow\infty}\dfrac{5}{n}\sum_{k=1}^{n}\left[2+\dfrac{5k}{n}\right]^{3}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes i agree with that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and the two is constant

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you just give me in converted? I like working back from the conversion

phi
 one year ago
Best ResponseYou've already chosen the best response.0I think of the 5/n as an increment (e.g. dx ) the k* 5/n ranges from 5/n to 5 for very large n, 5/n is close to 0, so k*5/n represents a variable x going from 0 to 5

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i do not understand what that means

phi
 one year ago
Best ResponseYou've already chosen the best response.0It helps if you have the "big picture" of how integration is summation of lots of thin triangles.

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1\(=\lim_{x\rightarrow\infty}\dfrac{5}{n}\sum_{k=1}^{n}f\left(\dfrac{5k}{n}\right)\) \(=\lim_{x\rightarrow\infty}\dfrac{ba}{n}\sum_{k=1}^{n}f(x^{*})\) \(=\int_{0}^{5}f(x)\;dx = \int_{0}^{5}\left(2+5x\right)^{3}\;dx\)

phi
 one year ago
Best ResponseYou've already chosen the best response.0I think it's just (2+x)^3 inside the integral
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