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bmelyk
Group Title
Express the limit as a definite integral over the indicated interval [a,b]
 one year ago
 one year ago
bmelyk Group Title
Express the limit as a definite integral over the indicated interval [a,b]
 one year ago
 one year ago

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bmelyk Group TitleBest ResponseYou've already chosen the best response.0
\[\lim n>0 \sum_{i=1}^{n} [2(1+\frac{ 2i }{ n }5]\frac{ 2 }{ n }\] over [1,2]
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.0
lim as n approaches 0 * if that doesnt look clear. looking for a step by step explanation.
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.1
is it like this \[\huge \lim_{n \rightarrow 0} \sum_{i=1}^{n}[2(1+\frac{2i}{n})5]\frac{2}{n}\]
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.1
we want to express the sum as\[\huge \sum_{i=1}^{n}f(c_i)\Delta x\] where \[\Delta x=\frac{2}{n}\]
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.1
we also wanna find c_i as the endpoint of each interval, \[\huge c_i=\frac{2}{n}i\]this means that we have \[\huge \sum_{i=1}^{n}[2(1+c_i)5]\Delta x\]
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.1
hence you can steal your function easily from that f(x)=
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.1
\[f(x)=2(1+x)5=2x3\]@shubhamsrg @ParthKohli
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.0
and is that the answer?
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.1
\[\int\limits_{1}^{2}2x3\]
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.0
so then i integrate normally?
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.1
yes but did you understand
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.0
yes i do thank you
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.0
is the answer 5?
 one year ago

sirm3d Group TitleBest ResponseYou've already chosen the best response.1
\[\Large \Delta x=\frac{ba}{n}=\frac{2(1)}{n}=\frac{3}{n}\]
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.0
i subbed in the wrong number
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.1
\[x^23x {\huge}_{1}^{2}=4613=6\]
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.0
so you're saying delta c is different than the other perosn?
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.1
i was thinking 3/n but its not even in the equation
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.0
im sorry i have to go to class but i will be back so please continue to explain further, thank you and chat soon
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.1
are you sure the class is {1,2} not {0,2}
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.1
so we should write\[\frac{1}{3}\sum_{i=1}^{n}[2(32\frac{3i}{n})5]2\frac{3}{n}\]
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.1
also 5(3) \[f(x)=\frac{2}{3}[2(32x)15]\]
 one year ago

sirm3d Group TitleBest ResponseYou've already chosen the best response.1
\[\left[2\left(1+2\frac{i}{n}\right)5\right]\Delta x=\left[2\left(1+\frac{2}{3} \frac{3i}{n}\right)5\right]\frac{2}{3}\frac{3}{n}\Delta x\] \\[f(x)=\frac{2}3{}\left[2\left(1+\frac{2}{3}x\right)5\right]\]
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
left side is stated as this correct? \[\lim_{n\to0}~\sum_a^b~f(a+i\frac{ba}{n})\frac{ba}{n}~;~i=0,1,2,...,b\frac{ba}{n}\]
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
gpt me i parts mixed around, and put abs in the wrong place, that summation
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
hmm interval (1,2) then ba= 21 = 3 so there seems to be a little confusion unless we are spose to factor within the given summation fo accomodate that
 one year ago

KatClaire Group TitleBest ResponseYou've already chosen the best response.0
@bmelyk @jonask it's [1,3], you typed it in from another question wrong
 one year ago

KatClaire Group TitleBest ResponseYou've already chosen the best response.0
@amistre64 @sirm3d ^
 one year ago

bmelyk Group TitleBest ResponseYou've already chosen the best response.0
yeah i fixed it.
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.1
so is it [1,2] or [1,3]
 one year ago

sirm3d Group TitleBest ResponseYou've already chosen the best response.1
then it's just \[\Large \int_1^3 (2x5)\;\mathrm dx\]
 one year ago
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