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Find the followings by definite integral:

(a) \(\displaystyle\lim_{n\rightarrow \infty}\sum^{n-1}_{k=1}\dfrac{n}{4n^2+k^2}\)

(b) \(\displaystyle \lim_{n\rightarrow \infty}\sum^{n-1}_{k=1}\dfrac{1}{\sqrt{9n^2-k^2}}\)

 Dec 29, 2016

Best Answer 

 #5
avatar+356 
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Nice! I'm 12 in 7th grade and at school I'm learning Algebra 2 but I skipped 6th,7th and 8th grade math so Algebra was like a whole other world for me last year! I dont have much time to learn new things. I am more into programming though.

 Dec 29, 2016
 #1
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What is that!?!crying

 Dec 29, 2016
 #2
avatar+9673 
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This is Calculus. My favourite branch of Mathematics.

MaxWong  Dec 29, 2016
 #3
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Dang, your smart! I have no idea how to do this stuff. I'm a beginner in Algebra 2!blush

NinjaAnswer  Dec 29, 2016
 #4
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+5

:P

Nope. I am 14 yrs old and school is teaching some Algebra 1. I learnt through all those Algebra 2, Geometry, Trigonometry, and Calculus all by myself :)

I started to know Calculus when I was 13.

MaxWong  Dec 29, 2016
 #5
avatar+356 
+5
Best Answer

Nice! I'm 12 in 7th grade and at school I'm learning Algebra 2 but I skipped 6th,7th and 8th grade math so Algebra was like a whole other world for me last year! I dont have much time to learn new things. I am more into programming though.

NinjaAnswer Dec 29, 2016
 #6
avatar+33661 
0

Here's the solution to (a):

 

.

 Dec 30, 2016
 #7
avatar+33661 
0

The same approach works for (b):

 

.

 Dec 30, 2016

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